You say that but the FIA are thinking of budget capping by other means. Kravitz said during his notebook after the race on Sunday that there were rumours that the new rules wouldn't include budget caps directly but would for example limit the number of specs of a front wing a team could have throughout the year. They hope by such measures that some teams could still have much more money that others but would have anything to spend it on.
The problem with budget caps is that the big teams can just go around them, having thousands of people employed by a myriad of different companies etc etc hiding/masking spending just like multi-national companies do to avoid tax.
Even preventing number of updates would just result in the big teams doing what Merc did in testing, literally developing a brand new car prior to the first race. Which again would make it so that the smaller teams cannot compete.
I think the only way you really drive balance within the sport is to fairly distribute the prize money.