The 2FA security is there to keep strangers from editing or removing stuff in your iCloud.
Say you make iCloud on the web accessible in a read-only version without 2FA, you eliminate the deleting and editing stuff, but still keep it possible for strangers to access your private information.
The best thing you could do is to write down the most important phone numbers on a piece of paper and keep it on your person at all times.
While the scenarios you think of are all stuff that can happen at anytime, I actually appreciate the way 2FA works in this case and wouldn’t want Apple to change it if it will affect protection and security in a negative way.
I can imagine dozens of situations where I can lose literally everything except what I can remember.
As I said in a situation where I have not lost my stuff, I don't need the Web interface.
And in a situation where I need the Web interface, I need my stuff to be able to use the Web interface.
2FA is great for security but without the Web interface, it would be even more secure. Why keep a Web interface around if users can only access it when they don't need it? I cannot imagine a situation where I have one of my iCloud devices around but would prefer to use the Web interface instead of the apps on the device.
I also have a suspicion that the four-to-six digit code on my phone is easier to hack than a 20-characters password of the Web interface. So if someone steals my phone, which I (and he) can use to access my data, why make it hard for me (and less fo for him, since he has my device) to access the Web interface?