If your iPhone storage is full, it won't allow you to update or download apps, take pictures, or even get new messages. Assuming you aren't partial to your texts there's nothing wrong with deleting them but comparatively speaking they're not very large files. If you're looking to clean up some storage on your phone, start with videos and applications first. Removing these will free up more space than deleting all of your texts (unless you have millions of messages which is certainly possible in 2021).