so first off, and sorry for the pedantism, cars are required to have three brake lights in the US. if a single one is out, it should be replaced promptly, but it is by no means an urgent problem. anyways, I don't want to debate this specific example in depth. if you don't agree, I'm sure you can think of some other example of an offense that gives legal grounds for a traffic stop but doesn't really justify it. frankly I am of the opinion that a lot of low-level violations (traffic and otherwise) exist primarily as a means to circumvent the default protection against unreasonable search and seizure, but we may just have to agree to disagree on that one.

the thing that strikes me as particularly tragic about these police shootings is how many of them started as confrontations over fairly minor offenses. would it be so bad to just let a few more people get away with petty crimes? or better yet, can't we find a way to hold these people accountable that doesn't involve a face-to-face encounter with an armed officer?

Older models might have 2 lights. Some motorcycles might have only one.

"gives legal grounds for a traffic stop but doesn't really justify it."

What do you consider justification? According to the law and police regulations, it would be justified. Logic also supports the idea that if there is a law on the books, it should either be enforced or removed. In this case the law has the purpose (as almost all traffic laws do) of promoting safety.

"circumvent the default protection against unreasonable search and seizure"

How so? As I stated before, the law's purpose is to promote safety. Also, when you sign your registration card or driver's license, you are agreeing to obey the traffic laws. This isn't just some made up excuse to violate people's rights.

"can't we find a way to hold these people accountable that doesn't involve a face-to-face encounter with an armed officer?"

We already do this for some infractions like red light cameras (what a disaster) and speed cameras. It's possible this could be expanded further, but probably wouldn't be able to fit all driving laws or areas. Also, what's wrong with the officer being armed? This shouldn't have any negative impact on the stop and should be reasonable since there is a likelihood that the person could be armed too, which most of the time is not also not a problem.

This is the year 2020 - I'm sure we can do better than this. If the police see a problem with your vehicle, there should be a way for them to look up your license plate and send you a notice, rather than stopping you in a way that could put both you and themselves at risk.

We already do this for speed cameras and red light cameras (a disaster). The main problem with just sending a notice for other things would be providing proof of the infraction. And even then, there would still be situations where the the is a safety concern that would be better met by stopping the person (stuff like DUI for example).