There should be both.
A vacuum that is not in any contact with any components and a good distance away to still be able to suck up particulates AND a compressed air blower to blow caked dust to free it from the stuck surfaces to be airborne to be sucked by the vacuum.
Over time, the fans push and compress dust to the nooks and crannies of the computer case, surfaces of the board, etc. To remove it, you need to have something to dislodge the accumulative pressed material. Consumer vacuums only have so much force, and it was not designed to remove materials that are stuck to an almost glue like state.
The best mitigation, is to implement intake filters and regularly replace or clean them ALONG with a blowing and vacuuming of the inside of the case. The reason why most fans stop working over time, in my opinion, is the combined dust that accumulates thus the fan needs to work harder, eventually giving due to working with the imbalance of stuck dust on the blades, bearings, and congestion.
That or watercool everything, sealing the electronic components from the outside, and thus only needing to clean the dissipating radiator and fans.
Grounding the components and cleaning while the computer is off is a must.