People with more connections can already get faster access to donor kidneys.
And a poor person with one kidney less but extra health checkups can probably get better health outcomes than a poor person with two kidneys but extra health checkups. (This assumes that the kidney sale comes with some mandatory regular health checkups. Just like kidney donations do.)
In Iran, there is no tracking of donors and most donors don't want to be associated with the donation long-term, as it's connected to their poverty and the shame of their poverty. In the limited surveys that have been done many also noted that they haven't been properly informed about the risks of a donation.
The time is gone anyway, and barring industrial accident you still have your entire body to sell again afterwards. That is not true of kidney donation — you can't donate a second time¹ and if your remaining one fails you are up shit creak because if you were in the position of being willing to sell one back then you are unlikely to be in the position to buy one now.
Donation of blood and other replenishables is a bit different of course, but allowing open sale opens some bad avenues in terms of people effectively being forced to (which could carry risks they wouldn't normally want to take).