MBP fan running but no airflow

I have a 2014 MBP, running very well but for one issue: the fan doesn't seem to move any air around, even though I can hear it running. As a result, the laptop gets quite warm, and further, it seems that the Mac throttles the CPUs to keep it from overheating (performance is one reason I got it in the first place).

I can hear the fan running (well, a fan-like noise anyway!) and the noise builds up when the load increases. I installed smcFanControl, and it shows the temperature and fan speed changing as expected. But no air movement. Running something like htop from the terminal shows CPU usage topping out at 60-70%. The CPU tends to sit around 60-70 deg C, which seems quite high for a permanent state. Letting in January cold air through the window only makes minimal difference.

What I tried:

• I restarted the SMC
• I opened the cover and looked for any lint. What very little there was, I removed, but there was no significant build-up in the vents or around the components
• I installed smcFanControl to see if I can tune the fan speed, the noise does respond to the settings but again, no air flow

None of it made any difference.

Any idea what the problem is, and how I can fix it? The laptop is working very well, so I'd rather keep it than replace it, even though it is getting old. Would Apple help at all - I never had anything fixed with them, but ofc the Mac is out of warranty.

I think the problem may have started around High Sierra upgrade, but it didn't bother me much at the time.

EDIT

It was suggested that this question is relevant. But I don't think so. I did clean the inside, and found no obvious sources of lint. Perhaps applying thermal paste would help, but I cannot see how, if the air is not pushed around by the fan.

How are you so sure that there is no air being moved around?

Further, when does the throttling apply - right at the start or after some time? Because at some point under high load, you will experience some throttling on basically any laptop.

The only thing - depends on how familiar you are with such things - I can think of, is taking the back cover off and literally looking at the parts. Yet, I would not necessarily recommend this.

Before doing something like this: Save your data either in a backup or by copying your files.

Apple might be able to help you, but what usually do and recommend is going to a certified repair shop. It's more personal and you usually speak directly to the repair guy. Though, I guess they will probably not be able to do anything different than what you did, @Tetsujin or I suggested.