XLR inputs are for mic levels. 1/4" inputs are for line level instruments. There are good reasons why you don't mismatch levels. Shoving line level outputs into XLR inputs results in a degraded signal because the input gain has to be turned down almost all the way to avoid overloading the mixer. Doing this means the signal to noise ratio is greatly reduced.
If that's your only option then you really have no choice, but the best way to handle a DI line level output is to use the 1/4" TRS input on the mixer.
It's clear there are differences of opinion here but I stand by my statements based on my professional experience.
That may be true in your experience with the gear you've worked with but XLR connections themselves can be for Mic or line level.
Many higher end boards especially digital ones like Avid SC-48, Midas , & Yamaha consoles only have XLR I/O on their stage boxes and / or the consoles themselves. These can accept either Mic or line with no problems.
You're correct that there are many mixer that have xlr for Mic & 1/4" TRS for line & sometimes those boards have pads and accept line level into the xlr input & some definitely don't play nice that way and 1/4" input can sound much better.
So it really depends on the specific consoles in question more than a blanket statement of XLR is always for Mic and line level is always 1/4"
Not trying to start an argument or anything that's just what I've encountered in my professional experience & trying to present as much info as possible so people can find what works in their situation.