Brendan Eich was making a point about the tab key also being used to switch to different text fields and buttons. This makes it difficult to type in certain applications. A space doesn't have that issue.
About your point of tab being represented different on different systems: It will always be ascii 9, how it's draw does differ between text editors but I consider that one of it's strengths for programming. Everyone can configure what an indent looks like for them, it makes reading code easier.
Having a non-standard size is exactly the reason the tab character (not the key) is unusable. If you accidentally get some space indenting anywhere in the same project as tabs, then it'll be misaligned on someone's editor and they'll "fix" it, making it misaligned on someone else's. Trying to never use space indenting is impossible. Never copy and paste from anywhere else, never manually align multi-line statements, never align comments with code, etc.
IMHO, issues with formating, like the ones you describe, should be cought by a linter. Or even better yet, enforce format-on-save in all editors your team uses and have it automatically re-indent and reformat the code so what indentation it was originally indented with irrelevant. I think this approach would work, but I tend to work on files < 10k LoC, it might get annoyingly slow past that.
I didn't even consider that, I just assumed we're talking about text editors.
But yeah I guess, that's another argument against getting accustomed to tabs for indentation.
Little irritates me more than logging into a new system, opening up code in vim, and witnessing the insanity of tabs-as-8-spaces
For me, it's not until that file is retrieved for local use where I have to deal with this. If it was born remotely and only used remotely with the same settings, I never notice it. But yeah, I hate it with the passion that raises my temp to that of a thousand suns.
The solution is to exterminate tabs, not hope everybody's settings are the same. I only code in editors that auto-convert tabs to spaces.