One equipment spec?
Cycling basically has this. UCI mandates a triangle template that all manufacturer frames must fit into as well as a weight limit and some other smaller specs. Therefore all UCI events conform to this rules (i.e. road cycling, track cycling, XC, etc). Many high end bikes, components, you buy will have a UCI stamp on them. Those that don't are not "legal" for UCI events. It's also mandated how the ride can "sit" on the bike (i.e the cockpit), especially in the time-trial, so that everyone is on "even" form.
Another well known one is cycling is Japan's Keirin events. This may be the most relevant to what your question is. Keirin specs stopped somewhere around 1980/ish. Steel frames, one real shape, no carbon fiber, etc etc. As classic a bike as a racing bike gets (i.e. if you draw a racing bike chances are you will draw a Keirin bike). This is track racing but it was done to remove the gear from the events so that it was about athletes (the culture around Keirin in Japan is like horse racing in the US, as in it's big on gambling/OTB and ALOT of money is made from it). Honestly, when compared to UCI events the racing is rather flat in Keirin. The strong/aggressive athletes raise to the front and win, even with the constant shuffling to "equalize" the fields). UCI events also do a Keirin event, though the rules/distance isn't exactly the same as Japan's, and the racing is FAR more dynamic.
This is why Ironman and Tri bikes look so out there is that they don't need to conform to any template and can do whatever they want.
Nordic skiing has requirements for gear, though it's loose compare to the UCI's
Swimming has suit specs.
Running has shoe specs (as of last year).
All of these sports already have a single ruleset. What motivation is there for a company to manufacture white label equipment, that is the same is everyone else's when 90% of why manufacturers sponsor athletes/events is to promote their gear?
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Outside of running... look at NASCAR/dirt track/modified cars vs. F1/F2/F3. Which racing is more interesting? Depends on what you like.
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For the LRC answer... I thought the right-wingers here hated "being told what to do" and/or "don't tread on me (unless I'm the one treading on you then it's ok)"? That comment is not political, socialism/communism/etc... it's about "freedom" (to choose) no?
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I personally would like to see spec racing in running. "Classic" gear (however that is defined) that is universal in the class IN ADDITION TOO the type of racing we have now. The reality though is that the spec class would probably attract only masters runners who want to try to relive their "glory days (when gear was simple)". No younger runner, looking for ANY edge, is going to race it especially if no manufacturer is offering contracts or sponsorship (which why would they, see above).