Would they though? The profit margin on replacing a gearbox is pretty good, just like Dba wages
The DBA's job doesn't generally extend to fixing your code to use database features correctly, write SQL in a sane way, etc. Even if it does at your company, unlike the mechanic they're not being paid by you to do that work; they get their salary regardless. So it's natural that if you keep bringing unpleasant work to them because you're bad at your own job, they're going to get upset.