After a bit of discussion, here is a consensus-based list of players where most random rolls might be considered "decent" or even really good value.

First come the G access Linemen rolling on primaries, that means Amazon, Norse, any human, imperial retainers, clanrats, thralls, skeletons and zombies, maybe even beastmen (they have mutations as well as options though) and all elves. The higher the cost of the player, the less likely you are to be willing to cycle them. But you aren't really going to cycle as most picks are good.
The vast majority of the skills available are things you WANT on your players, nevermind for 10k. A few are "nice-to-haves" and only one is kinda bad (shadowing) but its value might increase on MA7 lads, and even without it, just give a chance at that 1/6 stroke of luck.

After them we have again, on Generals, secondary randoms for any stunty lineman, be them goblin, skinks or halflings.
Block, Wrestle, dauntless, strip ball, tackle are all good picks, sure hands for sure, fend can find uses, frenzy pro kick and dirty player are all very useful, and even shadowing falls under the considerations above, especially on a skink.
One thing to remember is that now your stunties can just save up until they can roll a stat, that prevents your linos from bloating up with skills you don't actually want whenever they hit 6 spps. On the other hand you now have to try and keep them alive until they get to that 12/18 threshold...

Another predictable candidate are Black Orcs (not big uns) rolling random primary on Strength. They already have Grab and Brawler, and can't have strong arm, so what's left is a variety of good ones (mighty, stand firm, guard) some situational ones, and a couple objectively bad ones that anyway you don't mind for 10k.

Minotaurs also could roll for primary Strength randoms, for similar reasons, but they have only 8 to pick from because thick skull, mighty blow, grab and strong arm are out of the question, so juggs, stand firm, guard, brawler, multi block, break tackle are all decent picks you can use. Arm Bar for 10k isn't even that bad. You'll never use pile driver but that's probably a general consideration.

High Elf throwers rolling random passing COULD be decent because they already have 3 and of the remaining 9, only HMP is objectively bad (after the latest FAQs). Your thrower just basically picks up and sits in the backfield until it's time to chuck it with all those nice 10k skills that make his pass roll almost as good as before. Could it work?

Snotlings can do well on primary agility, because they already have dodge and side step... which you might say are the good ones anyway. But you can get value from Sneaky git, diving tackle, catch (with swarming) and a couple others. And they's so cheap that if you can't stand having a jump up, safe pair of hands snot you can just throw 15k at the "problem".

Still on the fence about rolling random Strength on norse linos, here the ground is a bit shaky and no more than half the picks are actually desirable, but people tell me you should have enough gold to cycle the wrong 'uns...

Beyond all this, I don't see many people going for randoms on other positionals. What do you think?