Whats the problem with justbdoing it though? Get a legally bulletproof waiver and you can't get sued
Hardly like we're running out of people
There are two reversible options for sterilizing people. One is a vasectomy, and outpatient procedure with minimal risk and local anesthesia. If you try to get it reversed and it fails they can get sperm out of you with a needle as a last resort. I'm not saying that is a good outcome, but it means you can still retain your fertility by virtue of testicles creating so many gametes.
The other option is tubal ligation, which is invasive, requires general or spinal anesthesia, and if reversal fails you are screwed, only one gamete matures at a time and it isn't practical to try to harvest it surgically. Essure was an attempt to make an outpatient procedure for female sterilization, but it seems to have a fair amount of problems associated with it and there is no reversal procedure for essure that returns fertility to a patient.
Women want to get sterilized to protect themselves, they risk so much more from pregnancy, and while that is understandable, it doesn't seem like a great option when so many reliable birth control methods are available to women (IUD, hormone pills) and vasectomy is available to men. Women's fertility is finite anyway, it will resolve itself given time, while men can impregnate women at any age.
Normal doctors like to do good work and improve the lives of their patients. Surgeons typically perform thousands of any given operation they offer to patients over a career. If one out of ten of your patients comes back to you for a reversal of an elective procedure, and the reversal fails a little less than half of the time, they're going to feel terrible about it eventually.
Some doctors who did tubals on childless women got sued despite their waivers. Juries are really sympathetic to cases where infertility is included in the damages, and the doctors lost malpractice cases despite the waivers. Perhaps that isn't fair, but it is the world that doctors have to navigate. Unless you have a genetic problem or being pregnancy is incompatible with you medically, there is no real reason to get your tubes tied instead of getting an IUD.
So yeah, there are a lot of reasons that things work this way. I am not going to deny that there are some sexist asshole doctors that use it as an excuse to deny patients care, but even in a sexism -ree world it seems like a good doctor would be hesitant to expose their patient to the risk of avoidable hardship.