> will lead to imbalance that could cause pain or bad posture

Citation needed.

It is a controversial suggestion that doing only one exercise as much as possible is not a good idea? Maybe these are relevant:

https://www.washingtonpost.com/lifestyle/wellness/muscle-imb...

https://en.wikipedia.org/wiki/Muscle_imbalance

Regular pushups cease being a strength-training exercise pretty quickly. You're being ridiculous. Once you're doing 40 in a set it's well into endurance territory, and you're not making muscles any bigger. It's like going for a run every morning, and slowly increasing distance as you progress, but for your upper body and in a lot less time commitment. We're not increasing the weight, probably decreasing it actually.

It's just at the start you're doing strength-training if you've never done upper body exercises, because your upper body is atrophied.

Also note I said ~maxreps, the tilde was intentional, it was meant to communicate "around your maximum" to express the importance of increasing it as your endurance improves.

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

So, what's a quick way to develop the opposite muscle group from push-ups?

You'd want to do a rowing movement, which is maybe a bit harder to do without equipment but you could do it with a rubber resistance band.

If you have a sturdy table or similar you can do inverted pull ups from underneath the table