I've a kidney transplant patient and also have been on dialysis previously.
The pain can come from fluid removal and electrolyte imbalances during the dialysis. The fluid removal is important because if you kidney fails, at some point you stop urinating. The in-clinic dialysis process is also compressing the 24 hour a day function of your kidney into a 3-4 hour process typically every other day. So if you remove fluid and shift electrolyte during a short period of time it can cause cramping and pain.
The situation can be improved by doing treatment over more days or for a longer period. That is where home dialysis comes in. Some people run it at a gentler pace at night. Some may run it for 5 hours 5 days while watching TV or doing something else. They get some flexibility around their schedule.
You can see one of the new home hemodialysis systems here. They are streamlined and less complicated to use than in the past. But for some older people and those with mobility issues they might not be operate it on their own.
https://freseniusmedicalcare.com/en-us/products/treating-wit...
I'll note however that I used a different type of dialysis called peritoneal dialysis which uses osmosis action of passing fluids through your peritoneal membrane in your abdomen. No needles involved but it doesn't work for every patient and over time it can stop working. But you end up holding a lot of dialysis fluid at night which can be uncomfortable. But it has less of the complications of fluid removal and electrolyte imbalance issues.
There is actually a project for a implantable artificial kidney but it has slow progress due to funding. This devices operates 24x7 do it could operate at a much gentle pace. Maybe its too ambitious but the lead scientist thinks about $50M would be enough to get it through trials.
Thanks for sharing your experience!