Maybe, maybe not. Given how lazily the dragons were behaving, and how they all ganged up on the same ship, it's not clear that most of the ships would have burned before they could escape. I don't recall Dany ever training her dragons to behave in a military fashion. I suspect getting them to focus on something she desires is a lot like herding cats. Maybe you're right and they have an unlimited amount of fire and won't get bored or tired of plinking ships. And maybe not.
Where you and I most strongly disagree is that they will equate surrender with survival.
Their minds aren't blank slates. They know well what victors do to losers in this world. They've been raised on such gruesome stories, not discussions of human rights and the Geneva Convention like we have. Prisoners of war have no rights in Slaver's Bay, and based on past practice in that part of the world, it's extremely unlikely that they will believe that Dany will simply release them unharmed with merely a stern warning.
There are worse things than dying. Again, the sailors on those ships are not omniscient. They don't have access to Dany's thoughts. All they can do is base their decision on what they believe a much demonized enemy will do to them should they surrender. You clearly have much more pleasant thoughts regarding the fate they would be imagining than I.
I expect the ones closest to the exit to order their oarsmen to immediately make for the open sea. And I expect that given how slowly Dany's dragons are operating, many of those closer to the open sea will be able to get away unless she immediately sends her dragons out to specifically target the ones that try to leave the bay.
They're not being atacked by dragons however. Another more distant ship is. Until their ship in particular is attacked, the smartest thing for them to do is to attempt to escape.
That's all the more reason for the ships to attempt to escape before the dragons get to them.
This is an assumption. I thought it was because she wanted to keep them all within range of her voice. It's hard to command someone or something that can't hear you.
Maybe. Maybe not. It really depends on how long untrained dragons are inclined to stay on task.
This is true if you're dumb enough not to take your armor off either before or after you jump overboard. Sailors don't wear armor however and as soon as it became clear the ground assault was aborted, the soldiers should have taken off their armor. Anybody who wears heavy armor on a boat when they're not about to do an amphibious assault is a total idiot.
Too pat. This assumes the Masters are total idiots which I suppose is par for the course for television, which is highly dependent on characters, most especially villains, picking up the IdiotBall to fuel heavily contrived plots. To entirely base the success of an assault, as well as the expense of all the material and the lives of all the men dedicated to it, including the lives of the Masters themselves, on an assumption like this is beyond stupid.
At least the buildings provided some cover against anything aside from a direct hit. The volleys seemed fairly random and not particularly accurate. It's not clear to me how staying just outside the wall would make them safer, since if the walls were hit, they'd fall on top of the people. I can understand people wanting to flee the city however.
But they weren't attacking the gates, they were attacking harmless people outside the gates. At least attacking gates would have served a small strategic value, I say small because the gates were on the opposite side of the city from the sea and weren't in between the attacking force and the great pyramid from which the city was run. Instead of helping win the battle, they seemed to be committing a pointless act of terror during the middle of a battle. This wasn't just an idiot ball, it was a full-out villain ball whose entire purpose was to give Danio and the Dothraki something to do.
Chosen to do something totally useless when there are countless more useful things they could be doing instead. It kind of cheapens a victory when your enemy is stupid.
Too many assumptions based on the villains being stupid and the dragons being all-powerful, when clearly as demonstrated in the gladiatorial battle that isn't the case, at least not unless it suddenly becomes convenient for the show.