And what might be negatives of having such a narrow tyre on such a wide rim?
Based on https://bicycles.stackexchange.com/a/52590/ a 25mm tyre is best on a rim with an internal width between 13 and 19mm.
If your rim's internal width is 25mm, then it is intended for use with a tyre from 40mm to 70mm.
The risk is that a thin 25mm tyre will end up more like a flattened curve. This stops the two parallel faces at the bead from forming a good interface with the crochet/hook on the rim.
An exaggerated view:
The consequences are a tyre that could feel squirmy under cornering, and since there's not a good connection to the rim, the tyre could part company with the bead at some point around the rim. The tyre might slip around the rim under braking and take the tube with it, which will tear the valve stem off.
I would not recommend doing this on someone else's bike. If you choose to try it on yours, do so knowing its not ideal, and don't complain if it fails and strands you a long-walk from home.
If the 25mm rim width is measured on the outside it should be safe. For example Zipp recommends a 25–28mm tyre with their new Zipp 404 wheels which have 23mm of internal rim width (27.6mm outside width). The idea is that having the tyre sidewalls flush with the rim improves the aerodynamics.
I don’t think there are any disadvantages. If aerodynamic drag doesn’t matter much for you one could argue that – to some degree – your rims are unnecessarily wide and therefore heavy.
If your rims are made out of carbon and therefore more susceptible to impacts the lack of protection by the tyre could be a disadvantage (only really relevant if you crash or otherwise abuse your bike).
I’d inflate to maximum tyre pressure (or even above) for a short time after installation just to make sure the tyre is properly seated.