Of course they did. When the rules dictate a 2.4 litre, four stroke, poppet valves - dictates the modulus of elasticity for materials used etc etc etc. It is probably not unusual for an optimal solution to be converged apon.
They all moved to V10s without outside influence. The FIA only had to lock in the V10, and later V8, design because of the murmurs from Toyota that they were going to use V8s, V10s, and V12s in the same car depending on circuit. Which frankly was never going to work and probably wouldn't have happened, but the FIA did the sensible thing to prevent people going too far afield.
Diversity tends to come from chaos. Look at the first years of GP2 and now Moto2. Since everyone is still trying to find their way in the dark there's 'competition' and it's all very entertaining. But over time GP2 races became more and more predictable as people found the best way to approach the weekends. Same as F1 strategy, very rarely do people deviate in pit stop strategy.
Look at something like CART when it was still an open format. A lot of the money was from tobacco, engine mfgs, or associated b2b sponsorship. So to an extent people weren't as performance based on sponsorship revenue. So people did wacky things. Newman-Haas subcontracted a bespoke Swift. AAR redesigned the Reynard to such ridiculous levels that it became an Eagle 987. Penske went pure prototype and made one of their most interesting cars ever. But it sucked. So did the Eagle. And the Swift wasn't worth the effort. So Roger goes to Reynards, cleans them up, and cleans out the points. Newman-Haas went to the Lola and once they unlocked the potential in that car everyone started migrating towards it. CART didn't need to mandate a particular chassis, they arrived at it.
That said, I thought CART had the ideal mindset chassis wise. Let the market determine whether bespoke, in-house, or customer cars are the best way to go.
The innovation found in motorsport is a marketing thing primarily. A small % of the F1 fanbase cares about the technology, and the majority of that subsection is ignorant of what's going on. They talk about double difusers, single keels, and embarassingly attempt driving technique. The actual tech nerds are a very very small part of the audience. I don't think opening up the technology is neccessarily good. Everyone is nostalgic for a 92 Williams, but that was a really dull season. And racing leagues survive on being entertainment, with as much technology as your customer base will allow. If you want to see wonderful widgets, watch DARPA or NASA.