If you have 4/2 (for same BPM)the half note duration is now equal to
Yes. The bottom number indicates the reference symbol used to measure the unit pulse. Therefore, half-notes are played at 120bpm. As others have suggested, almost zero musicians think of notes as durations of fractions of a second.
If that is so the lower number in time signature is really redundant.
For every rhythm you just have a reference note having duration equal
to beat time. And all other notes can be defined in terms of this
You are in part correct, and there are some composers would agree with you. For example, George Crumb:
You can see in the score that Crumb dispenses with time signatures completely, instead favoring a marked unit reference and a BPM. For this music, which is poly-temporal, time signatures are useless because different musicians are playing at different tempi.
Do you really need anything else?
Like many aspects of music theory, your stance that certain elements of time signatures are redundant holds up with certain types of music, but not others. For example:
In this image, taken from Crippled Symmetry by Morton Feldman, both numbers of the time signature are necessary because each instrument operates within their own metrical language. Because sound - and by extension - time are measured differently for each instrument, it is not possible to simply ascribe them all to the same pulse / unit beat and call it good. Each instrument is independent, and the music needs to reflect that.
Historically, BPM's were not used as a means of measuring music until the early part of the 19th century, 1816, upon the suggestion of Beethoven, who was one of the first composers to include the markings in his scores.
Broadening horizons, it's also important to note that not all music is measured with BPM, for example, non-Western European musics of Africa and India. In these cultures, especially the folk music, BPM's would be wholly irrelevant as the pulse and pulse-groupings shift constantly during a single piece.
So you see, your point is valid for certain types of music, and for certain aspects of music, but it is not valid for all types of music, and therefore your assertion that aspects of time signatures are redundant is only partially correct.
As a last thought, many conductors, when marking scores, do not even use numbers. Since they think gesturally, conductors often use triangles for triple meters and lines and squares to mark duple and quadruple meters.