Wouldn't a "Palestinian state...run and secured by Israel" actually be Israel?
Not necessarily.
Think of it as 'overseen', 'inspected'.
Which is quite sensibly the last thing Israel wants. Unless they want to paint huge concentric red circles on the backs of the overseers and inspectors.
Well a two state solution is what the US, the UN, and most everyone else are in favour of.
The pro-Palestine protesters worldwide seem to hate the Jews/Israel and want them gone, with a new state of Palestine being "from the river to the sea". They are demanding it all.
You are arguing that Israel should create an Israel "from the river to the sea".
That's one solution, with the Palestinians relocated to Muslim Arab nations.
Problem with that idea is that no Muslim Arab nation seems to want them.
If the US abandons Israel because it won't accept redrawn boundaries in a two state solution, from where will Israel then get its weapons for self defence?
There was a two state solution in 1948, but the Palestinians never accepted that, so they probably won't accept it today.
Looks like the perpetual war continues...no solutions possible.