"radio" implied to me that you are dealing with a multitude of signals
in that bandwidth, not just one, and my practical experience tells me
that you will have to deal with a wide dynamic range. What do you do
with the interfering signal that's 20dB above your signal of interest?
If you're wired between the source and the receiver with no outside
signals getting in, I wonder if you're engaging in overkill for the
receiver...

OK, so 1.25Gsps gets you to maybe 500MHz bandwidth. That's still a far
cry from 2GHz. Why would you be worried about the flatness over 2GHz
when your bandwidth is "only" 500MHz?

Of course, there are 'scopes available these days that sample a lot
faster than that.

Cheers,
Tom