Printing non-commercial model to make money
Intellectual property law is complex, so you might want to consider getting proper legal advice. However, to respect the original designer's intent you need to look at what their license permits and try not to find a loophole in the process. There is nothing to stop you asking the designer (in public or private) to clarify their intent.

The biggest 'non-commercial' restriction reason is to protect the design idea, and stop someone mass-producing a clever design for profit. This applies irrespective of the original designer's intent to monetise their work.

Another big reason might be to 'hold back' the time invested in the design. Maybe the designer wants to share something they spent a lot of time on, for individuals to appreciate rather than profit from. The designer would presumably gain reputation as a result of wider knowledge of their work.

Sometimes, a design inherits licensing restrictions from a 3rd party (even maybe from the design tools used). For example, Fusion360 can be used for free by small companies, students, or for hobbies and personal learning, but has restrictions on commercial, professional or for-profit use. In that case, you would need to ask clarification from the tool provider.

The case you describe is complicated. You can't sell the printed part, but a 3rd party can probably contract you to print the part (or rent time/access to a printer). However, your contract rate can't include any element of value derived from the model. Assuming there is no explicit license condition, you should be OK if you charge for your direct costs. As soon as you include time, profit, or any modification to the model, you are on less solid ground.

To consider a non-obvious use-case of the Fusion 360 license, a student may well not have their own printer (particularly for an exotic material, or living in university accommodation). Can they contract a fabrication company to commercially produce or evaluate their model for the purposes of education or not?

I don't expect you will find a definitive answer to this question since there are too many variables. Creative Commons have a page about their Non Commercial license which identifies some things to consider when you interpret a license.

As noted in the comments, you can divide your time and professional contribution (and thus billable items) into several steps. By providing a model, the customer skips step 1:


making the digital model
preproduction (slicing)
printing
postproduction (cleaning off support)


A clear license would refer to all of these.