Why do we tax public sector workers?

This occured to me the other day:

As the public sector HAS no money but what it takes from the private sector, is it not the case that applying tax to  public sector workers  necessarilly creates more public sector jobs to oversee the collection, expanding the state’s workforce that in turn requires more private sector tax revenue on the wealth-creating private sector?

I posted on John Redwood’s blog, in response to this, on that very point:

I have an odd question:

Does it make sense to pay Public Sector workers on less that 25k a year pay tax back to the Public Sector requiring more public workers to process it?

Would it not be more effective to simply pay them, having reduced their salary by an equivalent amount that they’d pay in tax, without pushing them through the PAYE system? The individual worker will lose nothing at all and the state should save money at the processing end at HMRC.

Or have I gone completely mad?

And then in response to some follow-ups, I sought to clarify my question by restating it:

Leaving aside notions of equal treatment between wealth-generators and rent-seekers, is it not the case that paying tax on public sector workers simply requires more public sector workers, and thus more tax on the generators, that were we to NOT subject them to PAYE?

There’s got to be a figure on what it costs to collect an individual’s taxes and thus how many tax payers are needed to create an HMRC deskmonkey. And if there isn’t, there should be, as this looks, to me, like a positive feedback cycle in the public sector that could be instantly eliminated with very little pain.