If you cannot download some media files from the iPhone into Photos for Mac

When syncing photos between devices or downloading media files from devices, it is essential that the operating systems on the mobile devices and the computer are compatible (Transfer photos and videos from your iPhone, iPad or iPod touch – Apple Support). The devices need to be able to understand the protocol and to confirm the trust. The computer needs to be able to handle the codecs of the media files. If the computer does not even recognise the mobile device as a connected device, try the fixes described here: If you can't import photos from your iPhone, iPad or iPod touch to your computer – Apple Support

But if only some files are missing from the Import dialog or greyed out, there may be several reasons for photos that do not download to the computer:

1. The format of the images and videos: A computer with an older system may not be able to download HEIC images, if the camera on your iPhone is set to use the High Efficiency format (Using HEIF or HEVC media on Apple devices – Apple Support) and the system on the Mac is older than macOS 10.13 High Sierra. Even if the system version is High Sierra, the hardware may not fully support high resolution formats, for example 4k video or very high frame rates.
2. The items on the device might be legacy media, that are no longer compatible with the current system version on your Mac.
3. iCloud Photos Library: The photos on your iPhone may be stored in iCloud and only mirrored on the iPhone in an optimised resolution. Then you cannot import optimised items from the iPhone but should download them from iCloud. Typically the video components of Live Photos might be removed by the optimisation, the depth maps of portrait mode photos, large videos or photos, that have not been used for quite some time. Use iCloud Photos on iPhone - Apple Support
4. Photos synchronised from a computer: If the photos have been synchronised to iPhone from a computer, for example with iTunes, they are not stored in the camera roll album, but stored separately, and the computer cannot download them. (Keep your photos safely stored and up to date on all of your devices – Apple Support). Synchronised photos are having many limitations. We cannot download them directly back to a computer, or edit them, unless we save a copy in the photos library on the device. To get synchronised photos back to the computer try to mail them or Air Drop them.
5. Photos saved from other apps are occasionally still blocked by the app. Then try to restart the device or reinstall the app.
6. The file system format: If you are seeing an error message about missing resources or unreadable files, and your Photos Library is on an external volume, check the file system format of the external volume. The format should be MacOS Extended (journaled) or APFS, not case-sensitive, and the volume must not have been used for Time Machine backups, and should be locally mounted: Move your Photos library to save space on your Mac - Apple Support
7. Missing permissions: If you cannot see any photos at all in the Import dialog unlock the mobile device again and when prompted, confirm on the device that it can trust the computer, see: About the 'Trust This Computer' alert on your iPhone, iPad or iPod touch – Apple Support
8. Security & Privacy Preferences: Ensure, that Photos for Mac has full disk access and access to file and folders in the System preferences > Security & Privacy.