Maurice Andre used to say that the period instrument movement had the "smell of the museum about it".
Playing natural trumpet is good fun. In fact I used to make my own and I am about to put all the instructions on my web site.
If you could play natural trumpet as your main instrument it would work out OK but switching between them would make dealing with the out of tune notes difficult as you would have to find some way to control the intonation.
I used to have an Eb cavalry trumpet that John Webb made up D and C crooks for:
It was great for doing things like Haydn symphonies.
Eb cavalry trumpets are very cheap and easy to find as "junk" if you want to play around with natural trumpet.