1A fuse instead of 1/2A fuse: any problem?

If you need to deviate you want something that will blow sooner rather than later. A 1A fuse won't blow as soon as a 0.5 amp fuse. It will tolerate a higher "spike" that might damage your equipment. Replace fuses as recommended by the OEM or with a lower amp rated fuse if you must deviate.

Actually you have QUADRUPLED the power that can pass since power is proportional to the square of the current.

Fuses DON'T blow at their rating. The rating is the current they will carry forever (almost). As current increases over the rating, the time until the fuse blows decreases. A half amp fuse will, depending on type, blow quite quickly at one amp, whereas the one amp fuse will not blow.

Put a 2a or a piece of wire in there, then you won't have to worry about those wimpy shutdowns.