Replacement for Quicktime?

So, why is there no new AV Foundation player app, showcasing the benefits of the new framework?

I assume there are several. (I.e., any current Apple multimedia app not based on the classic QT 7 MacOS structure embed.)

Or does QuickTime Player X use the new APIs?

As I understand it, "Yes." That is, it uses the AV Foundation structure for playback (and editing if required) of content IFF the content is programmed by Apple as being "compatible" with the app. I.e., if the combination of media file type and compression format is programmed to be recognized as being compatible with AV Foundation playback, then the content is played. If not, control is passed to the Modernizer MacOS structure embed to determine if the content is "conversion" compatible with the system as currently configured. If not, the attempt to play the media is terminated and an appropriate modal error message is usually issued based on error trapping results. Otherwise, control is passed to Convert MacOS structure embed along with the settings required for conversion. If the data is correctly converted, then control is returned to the original app and the AV Foundation initiates normal playback of the converted media content. Unfortunately, this process is not yet 100% foolproof.

And if so, then why is it missing so many features that are included in AV Foundation, such as MIDI playback?

Apple decides which AV Foundation capabilities and features are available to/included in a specific app's GUI. If you believe additional capabilities and/or features of the AV Foundation should be available to an app, then you should file a formal "Bug Report" (developers) and/or send a "Product Feedback" form (general users) requesting changes.

Are there any third-party AVKit player apps that anyone can recommend?

Not sure if you are seeking specific capabilities, features, or support structures here. Most people I know employ a combination of apps and utilities. I myself keep QT X, QT 7 Pro, MPEG Streamclip, VLC, HandBrake and a few more installed on my system. Each has its own advantages and disadvantages so I use the software most appropriate for a particular job based on the needs and/or requirements of the project currently in progress.

So, QuickTime Player X uses AV Foundation if it can, and if it can't, it tries to convert it so that it can? (Or just says it can't open it.)

While I did explain the entire sequence of actions in more detail than needed, what I tried to point out was, "Yes, the QT Player ('X' or v10 GUI) does use AV Foundation for playback but Apple decides what forms of data are played back natively, which may be converted, and which will remain totally unsupported." It would appear Apple made a decision many years ago to depreciate QT MIDI support when it removed instrument package and editing features from the "classic" Pro GUI version and has now totally dropped native support in the "modern" version. I am not a musician nor do I create MIDI files. However, I did, on occasion, enjoy modifying the efforts of others by changing playback instruments to suit my own personal tastes.

It just seems weird that QuickTime Player X is called QuickTime Player, and not AV Player or some such. And that it doesn't include lots of features that QT7 has, which Apple expressly wrote new APIs to replace.

The argument, for and against using the "QuickTime" name, was discussed extensively years ago. Most users assumed the new version of QT would simply extend its functionality by adding more support for modern forms of data compression while retaining its "legacy" playback and composite editing features. Unfortunately, this was not the case as Apple elected to abandon the use of multiple, highly specialized codecs in an "open" architecture in favor of the use of relatively few highly scalable codecs having an extremely wide range of use in a "closed" architecture and discarded many of the editing capabilities that made QT 7 Pro a viable "poor man's" alternative to expensive media editing apps.

QT7 is legacy, deprecated software, so it's crazy that it should still be a fallback for some file types, after so many years. Handbrake isn't really a player app is it? MPEG Streamclip looks interesting, though doesn't seem to have been updated since 2012 (beta) or 2008 (release)..!

Yes, QT 7 is a "legacy" player but it still "works" as a MIDI player at this time and I still use it for simple MIDI playback if needed when it's too much trouble to open a more modern and extensive app like GarageBand which offers the instrument editing options lost when the "classic" version of QT Pro was deprecuated.

No, HandBrake is a video transcoder. All of my videos are backed up as MKV files in their original compression format to 64TB RAID volumes. I then use HandBrake to transcode the content to H.264/AAC/AC3/Chapter M4V files for management by iTunes and Air Video HD "streaming." As indicated earlier I am not a musician, so most of my efforts are directed towards creating and maintaining my video library files which I am constantly updating and/or recoding to improve quality and save storage space.

Like QT 7 Pro, MPEG Streamclip is a "Legacy" player/converter supported by the "classic" QT 7 MacOS embed structure. Basically, it was the equivalent of a free QT 7 Pro app that lacked QT 7 Pro's layer compositing features but, unlike QT 7, does support transport stream content. I still use it primarily to create AV Foundation compatible MPEG/LPCM AVI files—a workflow I seldom resort to anymore. This app (like QT 7, QT 7 Pro, the QT 7 structure embed, and the Perian codec package, etc.) is no longer being "actively" supported or developed by Apple.

I suppose if I'm the only person who finds this odd, then that would explain Apple's inaction. 😁

Wouldn't go so far as to say that. Unfortunately, while it is obvious that you are frustrated, you have yet to make clear what it is that you want in the way of MIDI support from Apple. As mentioned above, my MIDI support needs are meager. I use QT 7 for quick "legacy" playback and GarageBand for AV Foundation support—to include the ability to modify playing instruments and/or convert MIDI files to AIFF (LPCM) AV Foundation compatible files which play equally well in either QT X or QT 7 player apps, as well as, iTunes. I archive these "master" files and recode them as may be require for specific distribution workflows. If you have different goals—such as the creation and distribution of MIDI (MID) files—then you may wish to search the App Sore or the Internet for an app having the capabilities and features that suit your specific needs and requirements.

Here are two videos demonstrating GargeBand playback. The first is of a MIDI file as downloaded from the Internet being played in GarageBand and the second of the same content but with a Chinese "Erhu" substituted for the track 1 "Acoustic Guitar" and a Chinese "Pipa" substituted for the track 2 "Acoustic Guitar" as modified by and playing in GarageBand. The last two sample file uploads are of 24-bit AIFF GarageBand archive exports to demonstrate their AV Foundation file compatibility. You can play, download, view, and/or test the files on your system if desired:

http://downloads.walker4.me/Downloads_files/ScreenFlow2.mp4

http://downloads.walker4.me/Downloads_files/ScreenFlow3.mp4

http://downloads.walker4.me/Downloads_files/Project2%20-%205%3A15%3A17,%2011.34. aif

http://downloads.walker4.me/Downloads_files/Project3%20-%205%3A15%3A17,%2011.27. aif

Apple supplies a lovely AVMIDIPlayer API -- I've written a CLI tool that plays midi files to Apple's default instrument samples in fewer than 35 lines of Swift. But wrapping that up in an app or QL component or Internet plug-in is beyond me.

This (the app and/or QL component ideas) actually sounds like a good solution if you can locate someone to collaborate with you on the project. Only other thing I've seen while browsing the internet are references to Mac users building their own version of the FluidSmith plugin for setup and use with the VLC media player—and that still doesn't address the QL issue.