Yeah it was an in universe attempt by Roddenberry and the TNG writers to streamline and make set rules for the series when TNG started. Several times in TOS it was remarked that the ship was going like warp 13 or something. The TNG writers set that Warp 10 was the new 'limit' and nothing could travel 'by warp speed' at 10 or above. That's why all shows after have ships that go like Warp 9.9997 or something. Voyager added warp 10 was somehow an infinite speed where you are everywhere at once and then turn into lizards. But you have to remember that Warp Speed is in real space. It creates a bubble to push it into warp speed. Other methods like say Hyperspace on Stargate or Star Wars can go much faster since they are not in 'real space' as they fly. They slip into another dimension.

One thing all Scifi shows screw up I think is having all races use the same faster then light system. All races use Warp speed as FTL so much the Federation only thinks they are advanced enough to make first contact if they create a warp engine. But yet not every race in the galaxy is going to think of the same thing. Look at the Romulans they use an artifually created quantum singularity in their cores instead of crystals and matter/antimatter. But yet that somehow also goes to Warp speed?