They ostensibly have this, a Resource Restriction Agreement. It does things like eliminate in season testing, which used to be very expensive, mandating a multi week summer shutdown during the middle of the season when no work is to be performed (even email is shut off for some teams). They also restrict time in the wind tunnel (even though most teams have their own wind tunnel(s), they can't use them all the time they are actually available, and limiting the computing power which gets applied to CFD in lieu of wind tunnel testing. There are a few notable things that don't get limited, for example, driver salaries, which can be very high.

In recent years, a lot of parts of the car are of a fixed design, and cannot be changed except for safety and reliability reasons. This includes the engine, the wheels and the main chassis monocoque (the latter is homologated at the beginning of the season). Chassis homologation caused a lot of teams problems in 2011 during the "f-duct" episodes due to teams having to find all sorts of clumsy workarounds to accommodate the ducting for the device without having designed space and openings for it in the homologated chassis.

Even the freeze on engine design (since 2007-2008 ish), has seen things like ferrari spending ridiculous sums to ostensibly improve the reliability of their oil pump, and oh, look at that, as a side effect, gain marginal amounts of engine horsepower.

Racing stresses components to their limit, on purpose, and fans don't like it when races are decided by attrition. So even well meaning attempts to limit development and restrict spending often fail. If someone has the money and the will to gain a slight advantage, it's hard to stop. Even templated designs and string limits on what development is allowed doesn't stop people from spending vast sums of money in search of tiny gains. Nascar is good example of this. While not all the spending is at the individual team level, you have large collectives and manufacturers doing things like designing their own suspension dampers and various engine optimizations. It's still extremely expensive in aggregate.

Easier said than done? E.g. what's to stop a team from buying a part from "some company" that only had one item in stock? Or what if all the engineers on one team decided to work for $1/year because they all got rich from something else?

It seems like you'd need a huge amount of regulation on the teams R&D process to prevent extra money from somehow being spent.

Aren't they spending a tremendous amount of effort regulating the tech as it is?

I know nothing about F1. It just seems more tractable to me to be able to have a single inspection item (the delivered car) at specified times (races) than trying to regulate the actions of thousands of people over years.

Limit how much money a team gets in prize revenue to progressive levels where even the losers can fund the next race, and restrain most of the revenue streams to funnel through prize money, and you effectively limit how much money a team is allowed to spend. Nothing else really does it, they just invite rule stretching.