"inventing new rules that are not there" is the problem. You keep demanding that things are explicitly spelled out in exacting language that leaves no room for anything else. Sure, the invisibility spell could have said it renders you impossible to see with normal vision. But since everyone who has read even a paragraph of fantasy knows that is what an invisibility spell should do.... is it really needed? Is "inventing" that "rule" such a necessity that the entire thing falls apart without it?
... No, not really. All of the functions of the condition work if you are just really hard to see instead of perfectly transparent. And forcing someone who cast the invisibility spell to make stealth checks isn't bad. It in fact preserves the utility of the skill check if you can't have a better version of it by just casting a spell.
Does being out of sight mean that you are stealthy enough to get the advantages of the invisible condition? Considering I've dealt with dogs barking their heads off while in a separate room... no, being out of sight isn't enough to make it so that someone needs to take time searching for where you are.
Would the rules be better if they stated that breaking cover broke the condition granted by hiding? No, actually. Because other than people insisting that the Invisible condition must mean transparent and undetectable, not just unseen, there are actual good reasons to allow the condition to continue after breaking cover. We've had a good half dozen of them proposed in this thread. If the rules insisted that if you leave cover, the condition immediately ends, then you would have to re-roll stealth every time you moved, which statistically means you are eventually guaranteed to fail stealth and get caught. And you should be able to do things like hide in the rafters, which doesn't technically grant cover, but logically makes sense to hide there, or slipping into a dark room, which logically makes sense to hide from humans, but doesn't technically provide cover, or disappearing in a heavy fog, which again, not technically cover, but makes sense that you could hide and stealth through a heavy fog. They left the rules open for actual, good faith, attempts at hiding and stealth. Not for bad faith "well, actually, the rules technically say..." play.
If you stop insisting they are broken, and stop insisting on scenarios that clearly were not intended... this all works perfectly fine, even very well actually.