DND_Reborn
The High Aldwin
You could of course, but as a core class I would advise against it. Once it is well rounded out, variant rules could be offered like other systems in 5E, but the main rules should be simple following 5E design philosophy.Should it be "simple"? In previous editions psionics has always been more complex optional "advanced rules".
Is anyone else other than @vincegetorix going to use these rules they're making? If no, then it doesn't matter how simple or complex they design them.
I think it only matters if you hope to encourage more people to use it. Again, I am only saying this as the base design ideals for 5E has always been (to my understanding) keeping thing simple and maybe offering variants for more complex rules.
From the start so far, I would certainly be willing to try adding a psionic character. This could be the basis for adding the psionc soul and other subclasses to the remaining core ones. (Personally, this is not something I favor, but I can contribute to the design so others can enjoy it.)