GWR does it but you get the same reject message whether all bike spaces are taken or one section of the route doesn't require reservations. It's utterly useless if you have one of these sections on your journey, since you don't really know if it's booked or not. They will usually check and reserve for you on Twitter.
Anyway, when you get on a Class 800, only one bike at a time* fits in the two bike spaces, which are probably full of luggage so it's academic. I've pretty much given up hope of taking anything other than a Brompton on a train now.
*tried with two touring bikes, 44cm dropped bars. The train manager watched and agreed with us it was impossible, GWR allocate the same width for two bikes as Cross Country do for one bike!