I have a couple of theories on why cruise lines are eliminating trays and in many ways it makes a lot of sense. Though it may be inconvenient,
I know when our family eats at the buffet its a big pain regardless of whether they have trays or not because I am rounding up food and drinks for two kids and myself, then d/h sits with the kids until I'm done then once I sit down he goes and rounds up his own grub and it is quite a production. If it were just food for myself its no big deal, I certainly don't mind making a second trip to get a drink, big deal! and with the sheer volume of food most people consume on a cruise it wouldn't hurt us to take a little walk in between courses. Oinkers aweigh!
First reason of all, having to be deliberate about what we put on our plate and sizes of portions since we only have two hands to carry it all with, probably cuts back dramatically on food waste, which is expensive to produce, prepare and then to have to dispose of it when someone's eyes were bigger than their stomach. This all costs money.
Lastly and most importantly, it helps control onboard infections. These days when you enter the buffet on NCL's ships you will encounter hand sanitizer you are expected to apply to your hands and then a person who is wearing gloves standing by the plates and silverware handing you your table service so that anyone who is carrying a bug (norovirus etc...) does not contaminate the stack of clean plates and silverware/napkins. Generally speaking trays often just get hosed down with hot water or wiped down with a cloth (I have seen this on more than one cruise line), but are not typically subjected to the same type of sanitation as plates and silverware and are more likely to convey virus's and bacteria because they are not cleaned as throughly.
For folks who have limited mobility or other physical limitations they can ask a staff member to assist them.
Unless I just want to grab something quick like dessert and a cup of coffee, buffets really are not my bag. On our last few cruises, I have not eaten a meal in one and find myself being served in the dining room, where I can sit down, relax and have a lovely, smiling, wait staff bring hot, steaming, made to order food to my entire family, while I don't lift a finger. Now thats my idea of a good time!