My other personal feeling is that it's easy to auto-check we aren't using tabs (just search for tabs, and reject if any are found).

Depending on how you choose to format, it can be arbitrarily hard to check tabs are being used correctly.

For example, many people want to do some space indenting, such as:

    <tab>void my_function(int arg1, int arg2,
    <tab>                 int arg3)
    <tab><tab>{

It's (I believe) impossible for a language-agnostic tool to know this is "correctly tabbed", but (for example)

    <tab>void my_function(int arg1, int arg2,
    <tab>                 int arg3)
    <tab>    {

Is not.