Can a layperson dare to handle the baseboards themselves?

That is not difficult. If you don’t manage the corners well, there are always these ready-made corner pieces. You just have to check beforehand if they are available to match the floor or the moldings. The same applies for the transition from molding to molding. Or use silicone. In new constructions with straight walls, it is definitely not difficult. We always glue with assembly adhesive, but for straight walls, these clip systems are not bad either.

and are not great craftsmen.

I only ever hear that from people who actually have an above-average level of skills in the downplayed subject. Just like: "Oh, sorry, it's so messy" - who would be wide-eyed in the spotless apartment before Marie Kondo "I'm so unathletic" - from the triathlete who just completed the Ironman "Just something simple, don't know if you'll like it" - when serving the 5-course meal that would make even Schubeck turn green with envy. I know my people! :P

If you want to keep it very simple, there are also plastic corners for the clip systems (color selection is rather limited to black, white, silver, gold) and you can simply insert straight-cut rails into them on each side. These are available for both inside and outside corners. Taste is subjective, but with the right color choice it actually looks acceptable.

Here is the version with the corner towers. I thought it was something different from the mitered corners or the beveled ones.

Corner towers: something completely different, nice idea, I like it

It would be interesting to know what cost savings you actually have when doing it yourself. For my 200sqm house, the labor cost of the craftsman was just 400 euros.