Not for sure but that changed last year at least or longer from what I remember.
I can only watch 720P as well in IE 11 Windows 7.
I will go and test this on my Lendows 10 Computer: IE 11 shows 1080P
All my Windows 7 IE shows only 720P
If you click the missing options on YouTube it will say 8.1 and higher is supported now. 
https://support.google.com/youtube/answer/6322658?p=missing_quality&rd=1
 
Below are some browser and operating system combinations that support YouTube's high-quality video formats:

• Google Chrome (all operating systems)
• Internet Explorer or Edge on Windows 8.1 or newer
• Safari on Mac OS X 10.10 or newer
• Firefox on Windows 7 or newer and on Mac OS X 10.10 or newer

 

No Clue, sorry

mike406
What if you use compatibility mode with youtube? That should allow IE to use Flash instead of HTML5 as Google probably is using a newer standard that IE 11 on Windows 7 can't support.

Yes and some do allow 1080P but Flash Player has problems.

Enter your YouTube settings and set it to prefer to use HTML5 instead and test.
 
https://www.youtube.com/html5
 

mike406

bcavnaugh

mike406
What if you use compatibility mode with youtube? That should allow IE to use Flash instead of HTML5 as Google probably is using a newer standard that IE 11 on Windows 7 can't support.

Yes and some do allow 1080P but Flash Player has problems.

The web will move forward. Either join or be left behind. His choice is to pick a more modern browser or make a compromise and use Flash.

 
Sorry I am Old School  I even use IE 11 on my Windows 10 Rig. If I could I would go back to IE 9.
 This is for 007vsMagua mostly mike406 for me 720P is fine for what is provide on YouTube.
If I have a need to for 1080P I would just watch it on my Sony TV

bcavnaugh

mike406

bcavnaugh

mike406
What if you use compatibility mode with youtube? That should allow IE to use Flash instead of HTML5 as Google probably is using a newer standard that IE 11 on Windows 7 can't support.

Yes and some do allow 1080P but Flash Player has problems.

The web will move forward. Either join or be left behind. His choice is to pick a more modern browser or make a compromise and use Flash.

 
Sorry I am Old School  I even use IE 11 on my Windows 10 Rig. If I could I would go back to IE 9.
 This is for 007vsMagua mostly mike406 for me 720P is fine for what is provide on YouTube.
If I have a need to for 1080P I would just watch it on my Sony TV

Sorry, I was speaking generally not toward you specifically. 

Nereus
 
Not worries with FireFox and W7... not sure why everyone here sticks with IE.
 

Not everyone has the problems with IE.

I suppose it is the problem of your VGA drivers. I had the same issue. Update it to the latest and try again.

007vsMagua
Found Fix:
 I gave up on IE11 and installed Google Chrome. I only use Chrome when using YouTube. I was then able to watch YouTube videos at full HD, but there was a problem with sound stuttering. I disabled unneeded plugins leaving flash enabled and I also turned off hardware acceleration. I'm now able to watch YouTube videos in full glory.
 _Thanks

Actually, you can still play YouTube videos in 480p and 1080p on Windows 7 Internet Explorer 11.  All you need to do is add this to the URL:
&nohtml5=1

Here is an example YouTube video to play.  The URL suffix &nohtml5=1 forces IE11 to use Adobe Flash and not HTML5.  Once you add this suffix, YouTube will play all videos you click on in Flash, as long as you don't click on a Windows 7 IE11 Internet Shortcut.  Here is where you can see if you have the latest Adobe Flash.  Here is where you can download the latest Adobe Flash.  You will need to visit this page in both IE11 and FireFox because each browser uses a different Adobe Flash downloader.  Always update to the latest Flash because it can have exploitable security flaws.  I don't know about Chrome.

Be aware, if you use Flash in YouTube, you lose the preview ability.  When you hover your mouse over the YouTube Flash player slider, all you see is a black box.  I use this feature extensively.  I have always used IE11 to play YouTube videos.  Because I no longer have the preview feature available, I now use FireFox for most YouTube videos.

The reason why Win7 IE11 does not support 480p and 1080p videos, only 360p and 720p videos, is because Windows 7 IE11 does not support "Media Source Extensions."  Here is a Microsoft TechNet discussion.  Here is Microsoft's Media Source Extensions developer guide page.  It says, "Important  This feature is not supported in IE11 on Windows 7."

Microsoft has been using various methods to get nonWindows 10 users to upgrade to Windows 10:
1.  How Microsoft's tricky new Windows 10 pop-up deceives you into upgrading.
2.  Microsoft accused of Windows 10 upgrade 'nasty trick'.

It has not entirely worked:  Windows 10 adoption is slowing, despite Microsoft’s best efforts.

Despite Windows 7's January 14, 2020 "end of extended support", Microsoft is not supporting Windows 7 100%.  I think not giving Windows 7 Internet Explorer 11 full HTML5 support is a result.  Perhaps this is another way of coaxing Windows 7 users to upgrade.  Windows 10 has numerous driver problems, including video driver problems so I will not upgrade until 2020.  Furthermore, Microsoft chose not to support older motherboards in Windows 10.  I think mine is one of them, Asus P7P55D-E.  Here is my desktop system (see the first and last 2 minutes).  This means, when Jan 2020 comes around, most Windows 7 users with older motherboards will no longer receive Windows security updates.

I tried installing WebM Media Foundation Components for Microsoft Internet Explorer but this did not fix the problem.  It appears only Microsoft can choose to give Windows 7 Internet Explorer 11 full HTML5 support.  Perhaps if users wrote to Microsoft and asked, they would do it.

Maybe we can help with that. What CPU do you have in your PC?

I have fixed the URL problem.  You can now read my post with the links.
 

Cypherdude
I have fixed the URL problem.  You can now read my post with the links.
 

Thanks, I'll be looking into it.