Why are some painful medical procedures done without anesthesia or sedation?

Risk vs benefit. Everybody has a different pain tolerance. Some people are too sick to receive much sedation. Keep in mind that sedation during procedures requires special training and increased risk from meds and added cost. Local numbing anesthesia alone is often the safest, cost-effective technique. If you feel that you need more, you can request to be scheduled.
No Excuse. Anesthesia & sedation require training. No excuse for not using these techniques to prevent pain in "painful medical procedures.".
Pain kills. Improperly treated pain can lead to chronic pain, anxiety disorders, traumatic stress, hypertentiion, high heart rate, and these last two can lead to death, heart attack and stroke. Many providers simply do not want to admit to themsleves that they are causing significant pain. They are not properly trained. All painful procedures should have good pain control.
Excuses. The key to your question is "painful". No painful case should be done without anesthesia if you mean pain control. If you mean by an anesthesia provider then the answer is they are not needed for all situations of pain control.And that would increase the expense. There are not enough to do all painful procedures. The danger comes when the non anesthesia person cannot relieve the pain.
I & D. Sigmoidoscopy is one. Injections or aspirations of fluids may be done without anesthesia. Drainage of small absesses or cysts is done without aneshesia because dead tissue does not respond to topical anesthesia ( i & d incision & drainage). When there is allergy or possible allergy. When the procedure is short and is more painful to inject the anesthesia than insert a sharp fine needle ( vaccines).
Bad care. Therecaret here is no excuse for a physician doing a painful procedure without providing adequate analgesia. It is due to ignorance on the part of the md.
Choice or pay. Some procedures need it but it still remains a choice when it comes to who pays for it? Not enough people raise the issue and the payors dictate the practice by not approving the procedure. Unpaid services add up and the hospitals and the facilities can not for ever cover the costs.
Talk to your MD. In some of these cases it is the decision of the surgeon to not use anesthesia or sedation. In other cases the sedation or anesthesia would not be paid for by your insurance policy. Talk to your doctor if you have any questions about a procedure.