We've had issues with almost all car rental agencies we ever rented from, Alamo, Avis, Hertz... all of them. So we have given up hoping for one that is all-over satisfactory. We had always booked the whole package from home, insurances and all, so really they should have just given us the keys and be done with it.
The first couple of times they kept pushing an upgrade we didn't want, plus extra insurances we didn't want, and they knew exactly that we - totally jetlagged - might not have the energy to stand their hour-long discussions at the counter.
The worst one was at Chicago airport. When they realized they weren't successful trying to push that expensive upgrade on us, they tried giving us a wreck. I'm not exaggerating. I knew exactly what the sound meant as I was driving a few feet on their parking lot: The brake linings were not simply worn out, they were gone. I'm not kidding. It would have been suicidal to drive this car.
During our last vacation, we had to use their service hotline once because the car wouldn't start. That was another catastrophe. I was passed on from one staff member to the next, each one more incompetent than the previous one. I really don't know what we would have done if the car hadn't decided to restart voluntarily after taking a small break.
In Spain, we tried to rent a car for one day only. The lady tried to convince us that we wouldn't need any insurance: "You're Triple A members, you've got insurance." I guess she thought all Germans were members of the related association (ADAC). Umm... no... in the first place, we're not members, and even if we were, belonging to an automobile club does not mean we have insurance for a rental car!
I don't know if these stories are any comfort to you, but as for "very unprofessional" - yes, you are not alone. As for "I've never had this happen anywhere"... unfortunately, all the time with car rental.
To balance that out, we did have a couple of really good experiences and very generous rental agencies. A rental car that got stuck in knee-deep mud on a Greek island... and the agency just took the keys without batting an eye, without charging us an extra cent, even though it was obviously our fault. Same thing with a rented RV I had managed to get a long scratch into.