I’ve only got experience of cruising on relatively small ships (i.e. fewer than a thousand passengers, so quite tiny by today’s standards), but on the most recent cruise last month I happened to chat with two people who’d had to see the ship’s doctor:
the one gentleman had had to pay a £100 call-out fee plus drugs costs, which was charged to his cabin (credit card) account. He was assured that he’d automatically be given a receipt suitable for a travel/medical insurance claim, as well as the amounts appearing on his cabin account. No idea what was wrong with him and I didn’t like to ask! The doctor’s call-out fees varied between something like £60 for a visit to the ship’s medical centre during the day, up to £200 for a call-out to your cabin during the night.
a 92-year-old gentleman was very happy to tell me all the ins and outs (not that I actually asked!) of his bout of pneumonia, which all sounded rather severe. The ship’s doctor gave him antibiotics and was prepared to get him into a hospital on land (and leave him there) if he’d taken a turn for the worse, but didn’t feel the need to quarantine him - which is something that can happen with infectious things.
Given how many creaking and elderly folk inhabit cruise ships, I’m fairly confident that ship-board medical staff can deal with all ‘standard’ illnesses for a price - so a UTI or chest infection aren’t going to faze them in the slightest.
Furthermore, your pre-cruise information should tell you what you are/aren’t allowed to go on board with, e.g. recent tummy upsets will see you banned from travelling and having to claim on your travel insurance. This is comforting, because it should mean that nobody with anything horrid is travelling with you!
I hope these second-hand experiences give you a little more confidence in cruise ships’ medical facilities and that you have an absolutely amazing time and thoroughly enjoy yourselves