The opposite is true, though. If you use tabs for indentation and spaces for alignment, you can adjust the tab width without destroying alignment. That's the big benefit of the tabs-for-indentation-spaces-for-alignment mix.

You can't do that with only tab characters, you can't even align stuff with tabs because it has variable width.

You might not understand how to do it properly so here's the idea:

Tabs will let you reach the indentation level of the current block, then from here, you'll use spaces to align stuff property. Here's an example, where >••• are tabs (I'm exaggerating alignment for the sake of the example) :

>•••if (condition1 == true
>••• || condition2 != false)
>•••{
>•••>•••struct ident people[] = [
>•••>•••>•••{
>•••>•••>•••>•••.name   = "bob",
>•••>•••>•••>•••.pubkey = "value1",
>•••>•••>•••},
>•••>•••>•••{
>•••>•••>•••>•••.name   = "alice",
>•••>•••>•••>•••.pubkey = "value2",
>•••>•••>•••}
>•••>•••];
>•••>•••secureConnection(people[0].name, people[0].pubkey,
>•••>•••                 people[1].name, people[1].pubkey,
>•••>•••                 CRYPTO_ALGO_DEFAULT);
>•••}

As you can see, everything will stay correctly aligned as long as it's within the same block.

You're confusing using tabs for indentation and spaces for alignment with using tabs and spaces for indentation. This means each line starts with tabs. Next you optionally have spaces for alignment with previous lines. Then you have content (like code or comments). Because you never have a tab following a space the alignment is never destroyed by adjusting how wide a tabstop is.