No! That's throwing the baby out with the bathwater! Removing all separators means rare-but-important manual tasks of transcription or comparison become terrible, since there are no clear chunks.
Instead use a different character which doesn't have the same problem, one that most software considers part of the same "word"... such as the classic underscore.
For most people, double-clicking on this 123_456_789 will select all 9 important numbers. (And maybe a trailing space, but that's a separate problem.)