Is it possible to clear all data off a deceased person's iPhone using a computer?

No. Without the account credentials, you won't be able to wipe the phone. If you want the phone wiped, you'll need to follow the link you posted from Apple, which yes, does require court documents granting you ownership rights to the phone. Otherwise, anyone could get their hands an iPhone and wipe it to use themselves, which Apple simply will never let happen.

If all you want to do is wipe the data and you're not concerned about being able to use it, you can put it into recovery mode and restore iOS using a computer, which will guarantee the data is gone.

If there'a a passcode on it, the data is not accessible without the passcode anyway. It's encrypted.

If you are not willing to go through the procedures to gain access so you can erase the device and you don't plan to use it then consider thoroughly destroying it. Without erasing the phone cannot be used by anyone including yourself.

A 10 lb sledge hammer would be useful in this case.

I suspect you could just erase it, but I don't think that would be 100%. Apple makes it easy to remove data from an iPhone since should somebody steal a device Apple wants to ensure data security. Along those lines, by the way, somebody would find it essentially impossible to get into the device unless they had the passcode. If they start guessing the code, the phone will lock and then anybody (including the true owner) who wants to use it has to erase it at the very least.

The reason I say not 100% is Activation Lock (AL). Simply erasing a device will not remove AL. If you do not want to use the iPhone yourself then you don't need to worry about dealing with AL. If you do want to use it then you do need to deal with it and that requires either knowing the username and password used to set up the iPhone, or making a request to Apple's special AL removal service to rest the device (which includes Apple erasing it entirely, including the AL setting).

I suspect you would need access to the phone. I wouldn't want somebody to be able to just pick up my phone and erase my data as a joke.

For example: How to factory reset your iPhone, iPad, or iPod touch - Apple Support

"If asked, enter your passcode or Apple Account password"

You would, of course, need to be able to get into the device first to be able to get access to the menu. I hate to be morbid but in these days of FaceID and TouchID it wouldn't surprise me if that was still an option.