the 1/4 note is mapped to the corresponding time interval per default.
Yes, this is because the quarter note is counted as the beat, the basic rhythmic feeling of the music. This can be changed to any rhythm that the composer feels best represents the feel of the song. For intstance, I could write a very fast waltz in 3/8 and site the beat as a dotted quarter note at 60 BPM, playing the beat only on the one of each measure, or I could write that same waltz at a slower 3/4 with a quarter note equals 60 BPM tempo, giving more weight to each individual subdivision. This drastically affects the phrasing of the song.
the 1/4 note will always take 1 s, no matter if I have a 2/4, 4/4, 6/8 or whatever time signature.
No, but with 6/8 in particular you are now NOT counting the quarter note as the beat, but the dotted quarter note instead. Quarter notes are not always the beat holder.
I would find the musical conventions easier to understand
No offense, but you aren't experienced enough to say whether it would be easier to understand or not yet. All of us had to learn how rhythms, time signatures, and tempo markings worked and we all worked through it just fine. Tempo markings are there to give a feel to the song, not only tell the strict time like a sequencer or DAW might do. Knowing how the beat divides the bar is an important element in phrasing, accents, and ultimately understanding the piece being played.
With other words I suggest to "rename the note values" as follows:
Again, this obfuscates the overall phrasing and structure of a song. Songs are built not from individual notes, but from strings of these notes which we organize into bars. It's similar to how we write sentences and then organize those sentences into paragraphs. If we called the sentences paragraphs then we'd still have to name the old paragraphs something, and it better be a better name than double paragraphs. In music we subdivide bars.
For another metaphor, think of an imperial ruler. You have 12 inches for every foot; think of this like a 12 bar phrase. Next you have within those inches four 1/4" inches, each subdividing the inch equally into four parts. Within those are 1/8" inches, 1/16", 1/32", 1/64", etc until we hit thousanths of an inch.
Let's say you were working on a project that was very small and you had to use the 1/4" for every measurement to make sure tolerances were in order. It could be 1/4", or 1/2", or 3/4", but you need them all. You wouldn't start calling these your 1 inch measurements, since you still are probably using whole inches as well.
In the end, working within the constraints of a bar and subdividing each works better at conveying musical ideas, the names not withstanding. If you feel the common 4/4 bar is not good enough you can change it, and put the emphasis on whichever beat you want. Writing in 4/2 or 4/1 is always an option. Changing the label/tool is not useful nor practical.