You'll regret getting strong and moving heavy-weight with bad mobility - you get those long term injuries you can't shake because now your own musculature is pulling things out of alignment too. The wrong muscles get activated in movements to overcome mobility flaws and they only get stronger and more dominant so it's like compounding interest on a debt.

I find that if I don't stretch frequently, squatting and deadlifting makes me tighter and tighter over time until I get injured.

You can't really get into the right positions, especially at the bottom of those lifts, if you have tight muscles from the waist down.

A major source of injury is not completely movements to full range of motion - not squatting below parallel, not locking out at the top of a deadlift, not touching your chest with the bar on a bench press or overhead press, etc. Not everyone has the flexibility/mobility to do that, but you're more prone to injury if you don't. So if you work a mobility program congruently with strength you will gradually get the mobility you need to complete the entire movement and not just part of it.