There are some, but there are several reasons that you haven't seen them about.

1. The people who spend the most on tattoos are doing so because they are art made by an artist. I'm not sure if you know many people in the scene, but these aren't the people getting flash tattoos at a random shop. They plan their tattoos, they pick their artists, and they spend many hours trusting another human to permanently alter their body.
2. The most common type of printers in the world print on a 2D plane, even most 3D printers are printing on a nearly flat 2D plane one layer at a time. The human body is largely not a 2D plane.
3. Human skin varies, ask any tattoo artist. You can't use the same pressure or the same type of needle on every person. And it takes people with experience to identify this. People who pay the most for their tattoos expect this expertise.

Those last two reasons are not impossible solves in any sense, but they do greatly increase the cost and complexity of a machine that can automatically tattoo a person without injuring them.

I'll also throw a number 4 in here. Speaking for the US, unless you've made a name for yourself tattoo artists are largely exploited here. They are mostly misclassified as independent contractors but then treated as employees. They are under valued and under paid.

So, how inexpensive can you make a machine to both purchase and maintain, while also being easy enough to undercut the already exploited labor in your average tattoo shop?

https://blackdot.tattoo/#introduction

It does.

With the lack of it existing comercial, why not make your own from a old printer like Emily the engineer did with a old 3d printer (youtube link)

What could possibly go wrong?

The YouTuber Emily the Engineer made one and tested it on her assistant, with success. But the video wouldn't make you want to try it.