Does it make sense to pay tuition fees for a PhD degree?
Nobody will ever know. In fact, nobody will likely ever ask you about this.
At the end of the day, for an academic career, what matters is that you have a PhD and have shown an ability to do independent research. Who paid for the PhD never enters these sorts of considerations: You may have been funded on grants and only done research, or you may have been a teaching assistant to get a salary and have tuition paid, or you may have paid for the tuition yourself. It really doesn't matter, and nobody will care. What people do care about are your qualifications.
Agree with the other answers saying no one will ever know how you funded your PhD. But, I don't see anyone addressing this:
When does it really make any sense to pursue a Ph.D. by paying tuition fees?
Blunt answer: very rarely.
- If you already have a job in industry doing research and need a PhD to progress, it could make sense.
- Ditto for certain, extremely competitive institutions (e.g., Oxford).
- Perhaps in some countries, the financial gap between funded and unfunded positions is less wide.
But I usually don't recommend taking an unfunded position, especially in thu US, because:
- Professorships and similar positions in industry are incredibly competitive. If you're not currently "good enough" to get any of the ~thousand funded PhD slots, you should be realistic about your odds of eventually getting one of the ~dozen faculty jobs in your field that are open each year. Of course, it is not impossible, but I would strongly consider other options with a better risk/reward ratio. It could even make more sense to spend a year or two strengthening your application and then reapply for the funded position.
- Fiveish years of tuition fees + living expenses is very expensive. Even with a high-paying job, it can be difficult to pay back that level of debt, particularly since many industry jobs (and quite a few faculty jobs) tend to be in a high cost-of-living area.
France
In France, paying tuition fees is not the same as paying for your PhD. This is just a technicality in terminology, but I think it's good to have this information for completeness.
PhD students in France are in a really odd sort of limbo -- French academic system is organised into institutes which work closely with Universities. The institutes provide the Professors for the courses at the University, and in exchange the University acts as a primary pool to get students in for summer projects, internships and finally PhD programmes; and also serves as a host institution for PhD students. This means that a PhD candidate in France is, at the same time, an employee of the institute, and a student at the University.
A funded PhD in France therefore means the following:
An external body (e.g. the French government, a foriegn government, or a company) will sponsor the PhD, ensure the funds for 3 years of (gross) salary, publication and travel costs, i.e. they cover the employment of the PhD candidate and expenses one is expected to incur during this time.
I'm not sure if equipment is something provided through this funding, or by the host institute. I think there's a good chance this funding might cover any visa or other immigration expenses, or the institute might, if you ask nicely.
The PhD candidate pays for yearly student tuition fees to the host University themselves. This is often a hidden cost which nobody remembers to warn you about.
Fortunately, this is a minimal cost: when I was doing my PhD, it was around €400 a year. Not a pleasant surprise when you're on a measly PhD salary, but definitely affordable, and unfortunately unavoidable.
Summary: Obtaining funding for a PhD programme in France is very competitive. Proceeding without funding would mean you are doing a full-time job for 3 years for no compensation, and since not even your publication costs or travel costs would be covered, I doubt any advisor would accept such a candidate. On the other hand, all the PhD students in France pay their own student tuition fees, which are however very low and affordable.