Have to disagree on this as its fairly evident over the last 3 decades, the tightening of regulations has increased the cost of F1 for all the teams hence why they (FIA) are trying to reduce costs by putting a cap on budgets which I think maybe open to secretive budgets within manufactuers with separate from F1 high performance facilities. When regulations are tight as per now with for example the engine spec (four-stroke, turbocharged 1.6 liter, 90 degree V6 turbo engines, Max 15000 rpm), engine manufacuters NEED to spend millions refining the tecnology to extract an extra 0.1% over their oppostion, with the opposition doing the same resulting in spirraling costs. If regulations where relaxed with the starting point of say 100 litres of fuel, no pre-stored engery (if teams choose to go hybrid), then each of the 3/4 engine manufacturers are able to explore their own designs and you'll get variations and likely the technology they develop will be more applicable to road applications which would be a large part in attracting and keeping engine manufacturers to F1.
A small example. In the last days of the v8's which had restrictions eg 3L and v8's, the teams I'm fairly sure were free on the bore, stroke, rpm limit etc and there was variation to the point that for example Renault was thought to be a bit underpowered compared to Ferrari and the others on power circuits but it was clear on some circuits (Monaco/slower corners), the Renault engine was better than others so while it may have been missing 30-50bhp top end, it seemed to have better traction and mid range grunt (Torque?) which will have been to a large degree due to the differing bank angle, stroke/bore etc. so what they lost on some circuits, then gained on others.
Summary: Variations in design would help produce different winners at different circuit types and probably reduce costs in the medium term given every teams starting point is the current spec PU but they'd be free to chop off 2 cylinders, add 2 cylinders, change bank/stroke/rpm etc to try gain advantage that way rather than millions refining the spec PU to gain 1bhp
I've seen in MotoGP where different engine design philosophies and even frame design philosophies have kept some manufacturers back for years until they eventually capitulate and make a 'normal' engine and normal frame/chassis.
RPM was limited in the V8 era, as were the materials able to be used to prevent exotic, expensive materials being used driving up costs. The current Hybrid designs have resulted in the most thermally efficient engines ever, and not just in F1 either. They're as much as 60% thermally efficient which is unheard of for an internal combustion engine. Your suggestion of allowing manufacturers to create whatever engine they like sounds amazing but again if one manufacturer hits upon the 'magic formula', as Mercedes did when the Hybrid era started then this drives up costs for the other manufacturers. In 2014 Mercedes won 16 of 19 races, with 11 1-2 finishes. 2015 resulted in 16 or 19 races again, this time with 12 1-2 finishes. In 2016 they had 19 of 21 race wins. People were getting bored and still are with the Mercedes and Hamilton Domination. People joke about 'HAM BOT VER' being a meme for something boring and predicatable.
If people want actual racing, tight regulations that result in teams coming together in performance as bigger, richer teams reach the zenith of performance earlier and then eventually other teams begin to catch up is the way to go. Changing regulations can give a chance for a reset in the pecking order but in all honesty it rarely happens, the richer teams can out develop the poorer ones even before the season has started. If you think Red Bull, Ferrari and Mercedes won't be towards the top end come the start of 2022 then you're sorely mistaken.