I also don't like those thick plastic-y feeling poly finishes.
Some poly finishes are ok, like my older Deluxe Nashville Tele has. (sunburst)
It's poly but seems thin-ish, and doesn't feel like the whole thing was dipped in plastic.
Being poly it will never "age" like nitro, but I'm ok with that.
If you are keeping it forever, then sure, strip it and have a nitro finish applied.
Only caveat would be, if you go for a transparent or semi transparent finish, like a sunburst,
you might be surprised at what is hiding under that solid color. (good or bad)
If you have it refinished in a solid opaque color, then it won't matter what the wood underneath looks like.
FWIW I stripped a cheap pawnshop Strat type guitar for the same reason. (thick plastic finish)
It ended up being plywood, so I did a solid opaque finish.
Good luck whatever you decide!