no encryption algorithm should ever be trusted without independent experts taking it for a ride and dissecting the cr*p out of it
Yes, that's a widely-held opinion.
And it'd be relevant if FourQLib contained any "new crypto algorithms". But it doesn't. It's a new implementation of well-known algorithms, using parameters and (well-known) techniques chosen to improve performance and other useful characteristics.
I've just skimmed the paper, but I don't see anything particularly novel in it - which is good. It appears to be solid, thorough work combining decades of research in finite-field arithmetic and ECC into a very nice implementation. They use some quite recent key results (see e.g. their references , , ), which is one reason why we will want to see analysis by other ECC experts, but overall this is evolutionary, AFAICT.
What it most definitely is not is a "new crypto algorithm". And, of course, as a zillion people have already pointed out, the authors work for Microsoft Research and have as much influence over the Windows EULA as I do, so your final two sentences are utterly irrelevant.