I'd say 95% of handicap runners and winners will be geldings by virtue of not being good enough to run in group 1/2 races therefore not being valuable enough to stand at stud.
I'm not sure the percentage would be as high as 95 percent.
I recently looked at a sample, which looked at the races of the winners I mentioned earlier.
From my sample, about 70 percent of runners were geldings, but they won something like 90+ percent of the races in question.
Some started their careers off as geldings, in which case there's not much to gauge. Others, (Withhold, Ghostwatch, Burnt Sugar, etc) are definitely interesting to look at, having improved beyond all recognition after the operation. Also, Ghostwatch was one of about 6 geldings contesting the 16 runner Melrose yesterday, he was definately in a minority: Whereas The Ebor was dominated by geldings, in terms of sheer numbers. The Melrose being a 3 year old handicap for younger horses, probably explains some of this, and relates to your stud theory.
The right horse/specimen it seems, after being gelded, can improve their ability, beyond what any form study can reveal, (certainly more than most punters might give this credit for.)
Obviously backing geldings blindly isn't a cast-iron way to making money, but you could say, that it's interesting to note, how many winners found their 'true potential' not long after being gelded, (and in a fair amount of cases), simultaneously changing trainers.
It's more of an observation, than a statistical analysis, but in many instances it does explain where the improvement has come from.
I personally couldn't back a filly or colt in a top handicap in England at present with any real confidence, unless it was a filly-only handicap like The Sandringham at Royal Ascot, or I thought the colt was extremely fast.
Crack On Crack On was about the only colt I could find, (there may be one or two others), to win a decent handicap this year.
John Gosden's Anna Nerium was one filly who won the European Handicap at Newmarket against the boys at start of the season, which I reckon takes some doing.
There may be more, but I'm referring to the big showcase handicaps, (or whatever else) they're called these days...