The 'favoured' riders / teams are on engines that are into the 60+ HP range, in the 125s. Singles only - the commentators that said they were twins are more than 2 decades behind the rules. The engines based on 125 MXers, dissapeared nearly 2 decades ago, as well.
For dirt use, you'd have to keep the revs up higher than MX 125 engines, once / if you could adapt to that (and blokes going genuinely fast on worked 250fs, are bouncing around the 10 to 13 +K revs) it would work on the dirt, but you'd have to be bloody talented. Not easy to use in the dirt, due to the Revs required to get into the working zone. That's the hard part with 125MX engines, the RR power spread would make it harder again. But, definitely blazingly fast if you could master it, and, if you could afford to keep it running. HP, costs, basically. If they could have been affordable / reliable to run, and easy enough for the average bloke to use, you would have seen 50HP MX oriented 125s.
The 250 TWINS, in the last years - the 'favoured' riders / teams were into the 120 +HP, just, from what a friend that worked in a 250 team told me.
As I've written many times before, we can blame Aprilia, just as much as Honda, et al, for the demise of 2ts in road racing. When it cost almost as much to lease a first line 250 2t twin, as it did to lease a Moto GP bike, it sure as hell made it easier to go for the 'cheaper' option of warmed over control Honda 600s (I think the engines are at a lower spec thank World Super Sport bikes - at least that's what I've read - how do you go from that level, to Moto GP 800s and 1000s, cleanly?), in bespoke frames. Same goes for the 125s - if you were not a 'favoured' rider, or team, you had / have, not a hope in hell of doing well.
'Controlled' class 125 and 250 2ts would have sorted this out, but the 4t push, is backed by the big boys. Controlled 125s, and 250s, of any stroke type, is what should have been implemented, if there was any sense to the FIM / Dorna series. Fat chance of that ever happening.