A better solution would be to stop overproducing PhDs. We could reduce funding for PhD students and re-direct that towards more postdoctoral positions - perhaps even make research scientist a viable career choice?
I'm suggesting that we re-direct some of the funding for training PhD students into funding for postdoctoral positions (via either fellowships or research grants). Professors would still get their research team, but rather than consisting mostly of untrained PhD students, they'd have a smaller, but more effective team of trained researchers.
Immediately after undergrad is how it used to work in the golden days of science, more or less.
If the competitiveness is the problem maybe tenure should be a lottery that you enter once at a fixed stage, preferably before you're expected to start publishing in journals.
A tenure lottery seems like an extreme option - there has to be a middle ground between what we have now and something entirely random.
The act of producing a doctoral dissertation usually leaves something of a mark on one's outlook, skills, etc. I claim it is a _distinguishable_ achievement for life.
In the past people who did science could do so with less personally on the line. In the early days you had men of letters like Cavendish who didn't really need to care if you liked what he wrote, he'd be fine without any grants. That obviously doesn't work for everyone, but then the tenure system developed for a similar reason: you have to be able to follow an unproductive path sometimes without starving. And that can mean unproductive in that you don't find anything or in that your peers don't rate your work. There'd be a gap between being a young researcher and tenured, sure.
Nowadays there's an army of precariously employed phds and postdocs. Publish or perish is a trope. People get really quite old while still being juniors in some sense, and during that time everyone is thinking "I have to not jeopardise my career".
When you have a system where all the agents are under huge pressure, they adapt in certain ways: take safer bets, write more papers from each experiment, cooperate with others for mutual gain, congregate around previous winners, generally more risk reducing behaviour.
Perhaps the thing to do is make a hard barrier: everyone who wants to be a researcher needs to get tenure after undergrad, or not at all. (Or after masters or whatever, I wouldn't know.) Those people then get a grant for life. It will be hard to get one of these, but it will be clear if you have to give up. Lab assistants and other untenured staff know what they are negotiating for. Tenured young people can start a family and not have the rug pulled out when they write something interesting.