Which isn't science.

There would be no scientific advance, if everyone would repeat every single experiment and grow old and die before they complete the last experiment.

they'd just do it too and have their own observation.

So why don't you start? Go ahead and sift through all the experements that were made.
Most of them were made thousands of years ago, so you should be able to do them with modern technology at low cost.

It was just a hypothetical possibility, to visualize how satellites floating around up there wouldn't mean earth has to be a sphere.

No!
They can visualize how satellites floating around the earth parallel to the equator could also float on a flat model.
Every other kind of satellite would at some point close to the south pole stop and change direction.

If it's always just the bottom we're talking about, I'm not sure that couldn't be other things like just a mirage of how our eyesight works when things are really far away on top of water.

You could use a camera then.
Also it isn't always the bottom. Or do you see the other coastline if you are farer away?

flat seem coherent and possible to me.

Really?
How would it be possible that distances on the southern hemisphere are about 3 times as long as on the northern hemisphere on a flat model, but still no one discovered something like this?
And still planes fly a much longer way than they would, if they were flying on a flat earth? That would be very expensive, don't you think?

They had their senses, they had reasoning capacity.

That's why Erasthosthenes already measured earth's radius over 2000 years ago.

I think it's easy to mistake "I'm used to thinking about it this way.. I can't imagine that what they told me in school is wrong" with actually observing it.

As I said I don't know any flat-earth theory that is coherent and therefor only a globe is reasonable to me.
And at the moment you didn't give me much concrete information on that "coherent and possible" flat earth model.