This is just an interesting idea that sprung to mind to me earlier today. After watching last nights 2020 Final and seeing who the next seasons line up will be as it was released not long after the final I had a thought of maybe a former BGT Contestant could compete regardless of how far they got in the competition, as I don't think any have beforehand. So my mainstream ideas could include Jess Robinson (Spitting Image is like a comedic satrical show so due to her voice overs in the show I'm including her despite her being an impressionist on BGT), Jack Caroll perhaps could be interesting, Daliso Chaponda (He's recently done Royal Variety so hopefully he'll be a big enough presence at some point soon in the world of comedy for the show), Cal Halbert from The Mimic Men (He was a comedian before he became an impressionist), Alfie Joey from The Mimic Men (I'm including this impressionist as I'd find it interesting to see if he'd have any sort of arguments or disagreements with Halbert whilst competing against him, so clearly these 2 would need to be in the same series and come as a pair), Robert White, Mickey P Kerr, Darren Altman, Chris Leworthy (I'd just like to see more of this guy, and I kinda want to see what he'd do on the show to be honest), Ben Langley (Similar case to Chris here), and maybe Andrew Fleming Andy Storey (Although maybe Storey may need a few more years in order to grow his career prior to being on the show), Kojo Anim (Similar case to Storey however though) & maybe Lost Voice Guy.
However I'd only want about 1 BGT alumni in most cases however 2 in Halbert & Joey's case, and probably prefer this occur every other Series or 5 randomly being picked for a 1 off special, or if BGT bought 5 back for TaskMaster skits but I think the latter idea would just be completely weird & bonkers and it'd probably lose some of it's charm without Greg & Alex.
So these are my opinions and suggestions on this strange idea that I had, and as usual if you'd have any thoughts on the matter please feel free to state them. Just a sidenote here but the comedians and / or impressionists that you pick can be from any series between 1-14 of BGT so you are not limited to a single series and can feel free to add as many as you like to your list, you can also add your own reasoning as to why you want them on the show or why you think they may be ready to appear on the show, or if you think it'll be a while before they are on the show etc.