What do you do with that famous place in the middle of the first movement, the recitative, where Beethoven marks a single pedal held all the way through? It worked on his piano, and gave a sort of fuzzy, far-away effect, but the sound decay was fast enough so that the music remained clear. But try taking that pedal marking literally and do that on a modern Steinway model D concert grand, and see what happens. The recitative turns to mush.
Only a few literal-minded pedants would do that today. Most pianist use a half-pedal, and use finger-pedalling, holding as many notes of the chords with your fingers as possible, to approximate Beethoven's effect.
Once in around 1970 in Baltimore, I was playing this sonata in a short recital in a senior citizens' center, to inaugurate their new Yamaha baby grand. Just at that spot in the sonata, where I was trying for soft, half-pedaled effects, someone who was not a concert attendee came clomping into the room (it was the rec room in the center), went over to the soda machine, loudly dropped her coins into the machine, took her soda can and clomped out! I thought, "I'll kill her. I'll find out who it is and I'll kill her!"
We pianists deal with all kinds of problems. At least this was somewhat humorous.