A cost cap of $XXX,XXX,XXX will never work. But the regs could be written such that certain items need less investment. Would the following really make F1 that much technically limited or less intersting to watch?
Spec Wheels and wheel nuts
Maximum of X controlls on the steering wheel
Spec steering wheel
Spec engine attachment points
Massivly tight regulations on end plates
Specified wing mounting points
Massively simplified brake packaging. Have you seen the carbon fibre cake tins around them?
Two (dry) tire compounds for the season. In 2017 Pirelli took an average of 13,000 tires to each weekend. That's nuts, if we don't' have a tire war why do we need seven, yes 7 different dry compounds?
Price cap on engine leases and a requirement that each engine supplier has to supply at minimum two teams and be prepared to supply up too four teams. That way if Renault, Ferrari, Mercedes or Honda want to spend $200,000,000 developing an engine they can, but the teams can still afford to race.
I get it that hybrids are here to stay, but what about an off the shelf hybrid and / or battery pack? They get up too 160 equivalent hp from the motors under full tilt. Make that spec, who cares, they still have the differentiated engines. As an aside this could help stability as Ferrari are currently under investigation for finding ways around peak energy deployment.
Minimum engine and cooling inlet sizes
etc.
The famous 1992 Williams FW14b is still regarded by most in the sport as the most technically advanced car to have raced in terms of on board technology. Back then Williams had one of the largest Budgets at (supposedly) £25. Converted to $'s and adjusted for inflation that's $68M USD in 2018. A lot of money, but chump change in F1. The difference between then and now is that with the last hurrah of tobacco money and a good economy through the 90's budgets were (essentially) unlimited and millions upon millions were spent chasing those last 0.0001 of a second. Give every one a tight rule book and let them have at it, but limit the things that are pointless dead ends so the money can be spent else where and less is needed.
Oh, and don't be scared of Ferrari leaving, if they go fine, but don't cave on cost cutting to keep them. I honestly think Ferrari need F1 more than F1 needs Ferrari. Porsche have built their whole brand around Sports car racing and even they've taken brakes from it. Ferrari essentially walked away from Sports cars circa 1970 and built their whole brand around F1. They might leave, but I'm sure they'll be back.