The background

I am training for running and sport climbing; I also have a good barbell rack in the basement and have good technique for the "big 5" barbell exercises (squat, deadlift, bench press, barbell rows, overhead press) from doing them a lot, a decade or so ago.

My 2023 running volume was 1200km, running 3-5 times most weeks, following structured training plans with a sub-2h HM PR. In parallel I climbed 2-5 times a week (UIAA 7-8 on rope, French 6a-b bouldering), and done regular full-body mobility, flexibility work; and very occasionally some additional running-specific strength training.

The focus of this question is injury avoidance, not competitive race results. My primary goal for running is to be able to do it as much as possible without injury (because I love it very much); I do race regularly, but only against my own results.

The issue

On the one hand, I want to do more strength training again for its own sake; mostly because, well, I like to be strong, but also because I'm in my late 40s and like to prepare for the years to come.

Secondly, I have a sedentiary job and am not a "natural" runner, i.e. when I started out I had plenty of joint issues, which I fixed completely using running-specific exercises (some body-weight strength, mobility etc.). I wish to avoid running injuries as well as possible.

Obviously, when looking for running-related strength exercises, one finds primarily body-weight routines targetting especially smaller muscles (or often underused ones due to sitting a lot) that tend to lead to imbalances and running injuries if week. Or even barbell-based sessions that are quite different from the "big 5" barbell movements I've mentioned above.

But as much as I love and adore my two main disciplines, and barbell-based training, I really do not like the running-specific strength sessions beyond using them for a few weeks to fix something that pops up. I understand that they are, well, specific to running, often targetting tiny little muscles that are not really the focus of the big barbell movements; I understand very well that they are probably the best one can do, time-efficiency wise and so on and forth. But a strength routine I'm not doing because of motivation issues is not going to help me.

The question

Will doing the "big 5" classical barbell exercises (squat, deadlift, bench press, overhead press, rows) to a reasonable level of weight (for example, let's randomly say roughly body weight on the bar, for squats), eventually in long-term maintenance mode (maybe 1-2 sessions per week once a reasonable level has been reached) be at least somewhat worthwhile for avoiding running injuries? Or would they actually lead to further imbalances that would force me to do other running-specific strength exercises for some smaller muscles to keep up with the big ones, but now even more so since the big muscles are even bigger now?

Or should I put this plan to rest and focus on finding a more running-specific strength routine that I really like to do, instead?

To be clear, whatever the outcome, I would still be continuing with my regular full-body mobilization, balance, stretching routines etc.