Why don't light-up runway numbers similar to runway lights?
Because it is fairly easy to determine which runway is the correct one by other means.

Runways are numbered based on their compass direction. The runway number will be the compass direction divided by 10 - for example, a runway with a direction of 150 degrees would be numbered 15.
This makes it possible to verify that you are using the correct runway by simply looking at your compass, to make sure the runway is pointing in the right direction. Even during day time in nice weather, this check is routinely performed before taking off by most pilots.

Runway identifiers for parallel runways are suffixed with an 'L' for the left runway and an 'R' for the right runway (from the pilot perspective). At airports with three parallel runways, the identifier of the middle one will be suffixed with 'C' for center.
When approaching an airport at night, the runways will - as you point out - be clearly lit. It is easy for the pilot to spot any parallel runways and make sure they are approaching the correct one, simply by observing the relative position of the runways.

During night or periods with degraded visibility, most traffic will make use of precision instrument approach systems, such as ILS, which will guide the plane precisely to the correct runway, without much risk for confusion.

On the ground, clear airport signage make it nearly impossible to mistake which runway you are on.

In addition, at busy airports with multiple runways, air traffic control service is likely to be provided. Air traffic controllers will monitor all aircraft movements on the maneuvering area and in the vicinity of the aerodrome, and will quickly be able to notify any pilot who is about to use a wrong runway.

Another point is that lighted runway numbers would probably be pretty ineffecient, as the relatively small size of runway numbers would make it impossible to read them from a distance, even if they were lit. A pilot approaching a wrong runway would notice this too late to be able to make corrections, and would have to perform a missed approach. Granted, doing so would in many cases be better than landing on the wrong runway.