I played mostly cash games and was lucky because I played at a casino that if I didn't like something could just get up and go to another table and be able to play the same cash game stakes, lol.
I wasn't playing at a 8 table poker room that closed at 11pm or something for the cleaning folks. I would just take a walk or go to the farthest table away, far away, if I didn't like the smell or something happening at the table, lol, far away.
Never experienced "greasy" chips before but had spoken to people and heard tales about that but I always carried something like wet napkins, and tissues and of course the easiest thing would be to just exit to the bathroom and wash your hands so no big deal there if playing cash games.
I rarely if never had to wait to wash my hands at a casino so that was an option as you just tell the dealer "sitout" and they watch your stack until you get back.
As for getting food on things, the cards get a hole punctured in them and go to the gift shop and the chips would get washed anyway. I never had something "nasty" on them to the point I would have to ask the dealer to switch it out cards or chips because of that.
And to be honest, if you ever go to a public bathroom and see how many people come out of a stall and don't wash their hands then worrying about food or something would be the last thing on my mind, lol. I would never, ever touch my face during a session, lol.
Nastiest thing, where you're in a really nice casino bathroom (not like a truck stop bathroom where some trucker is washing their feet in a sink, lol) and you have clean floors with the soft music in the background and the sinks, soap and towel dispensers are automated so you don't have to touch them and I would STILL see people come out of a stall and exit without washing their hands, lol. JUST FOUL.
As for the tourn folks, I'm thinking there is no way you could tell the tournament players they couldn't eat at a table and I was never a tournament player.
They would not have the time to transverse the poker floor and the casino floor then wait in a line, wait for the order, sit down to eat then walk aaaall the way back to their table outside of a dinner break. And heaven forbid there is a wait at a casino restaurant, (sarcasm) lol.
So they would have to order at the poker table or eat what they brought along and eat there or miss hands and that's the last thing anyone wants to do with big blinds and antes going around later in a tourn.
And a lot folks want to use that dinner break not to eat but to go to the bathroom, relax, unwind, take a nap, meditate or talk to friends on what's going on during a tourn. Wasting time traversing a crowded casino floor looking for food would be the very last thing on my mind even though its called a "dinner break".
Even if you play local daily tournaments or weekend tourns that finish the same day there are instances where those tourns will start late morning or 12pm and still go early into the morning hours while the dinner break was waay back at 6pm or something so people need to be able eat and drink at the table.
If the sight bothered me then I would look at the felt/their hands if they're right across from me or would add a hand towel to my bring along bag so I could put my head in my hand with the elbow on the table so I don't smell it so much but overall I would just understand that some people need to eat and cut them a break.
You have to be able to eat and drink small meals at a table to keep going during a long session whether its cash games or tourns and you also don't want to just load up at break time then get all sleepy and tired from eating a large meal when you have to play for another god know how many hours until the tourn concludes or if the cash game is going good.
And again, break was early last night and its 3am the next day and you're playing to a conclusion or a high roller just sat down to your table after having a losing table game session and wants to play poker and you haven't eaten in awhile and the tourn director or dealer is going to say you can't eat? And you're playing for how much money? lolololol yeah.
Tourn director/dealer should be asking how folks are and asking if anyone needs a menu, lol.