Mildly Interesting

No-ish. There's something to it, tho: The more users on a carrier, the less bandwidth available per uplink. With VSAT (which pretty much every large ship has), this isn't really a problem, as there's plenty of bandwidth available. Bandwidth allocation is pretty expensive, so most ships cap their bandwidth relatively low. With the ships I work with these days it's usually between 0.5mbit/s to 2mbit/s. I've never seen this degrade when entering high traffic areas.

With starlink there's a bit more to it - I installed one of the first offshore starlink antennae, and back then it was insanely fast. Nowadays there are a lot more starlink terminals around, so it's not that fast anymore. So in general, bandwidth is a lot lower per terminal due to the large amount of customers, so a large ship or two nearby probably won't make much difference. Large ships don't get more bandwidth just because they're large. But it's common that they have several terminals (I usually installed two per ship), but that's mostly for redundancy and avoid that the ships superstructure comes between the dish and the satellite.

As for pirates disabling AIS, I doubt they have AIS to begin with. I used to work in nigerian waters, and the pirates in question usually use very small boats loaded with fuel for endurance. We're talking something that is marginally larger than a hollowed out log with an engine strapped on it. We used to call them "war-canoes".

Locked out of comms: Depending on what you call comms, this doesn't really happen. Sure, internet can go out (and it sometimes did when I was offshore myself), but anyone who might need to reach you in case of emergency know how - Usually by calling your employer. There's a myriad of ways of talking to someone onboard a ship. Normal internet is the most common nowadays. If that doesn't work, they still usually have phone service. And if that doesn't work, it's actually possible to route phonecalls via MF or VHF radios (expensive as fuck, though). And if that doesn't work, there are things such as Telex that enable you to send text. The available hardware depends on the ship and which areas it's rated for, but it basically boils down to ships being required to have comms equipment that enable voice AND text for the rated area. Near the polar regions this basically means Telex and HF radio. For anywhere else, this usually means MF radio and Inmarsat.

Fun anecdote: A coworker of mine, during a period of no internet being available, was instructed that he needed to head to the bridge ASAP due to urgent communications from home. I was his shift leader at the time, and it was not a fun message to relay, as we knew this often meant serious illness in close family. We were all relieved to learn that it was just his dad who had come across a really good offer for a quad bike, and my guy onboard needed to let him know yes or no within the day.

Just to clarify, as this overlaps with several jobs I've had, including my current one:
2008-2012: Offshore seismic survey tech.
2015-2019: Maritime comm and navigation tech 2020-Now: Support/IT dude for offshore seismic survey hardware.