I've had some horrors, mostly before I realised that 'setup' was even a thing you could do. I remember as a teenager stringing up a telecaster with 13s tuned to standard and then wondering why the action was so high. Amazed the poor thing didn't just fold up, but it held on heroically until I went back to standard gauges with no apparent lasting damage.
I must say the amount of years I spent afraid to touch a truss rod would have significantly smoothed my learning curve! I'd also probably own a fair few basses and guitars I sold on because they had "issues" that could have been easily fixed...
13's will take standard tuning just fine thank you. I even tuned them EADGCF for a while.