But your muscles don't have to become very strong to get imbalances. You can get rounded shoulders just from sitting with a hunch at a desk all day. Imbalances in your pecs and back can cause shoulder impingement which is a common injury. Tendonitis is also easy to get when starting running, especially if you go for your 'max distance' based only on what you feel you can do.

Strength training is often advised to prevent running injuries, eg. https://www.runnersworld.com/health-injuries/a20788889/fix-m... which is particularly related