Pension and tax relief - dumb question!

[Mouse]

Here's what I know......

You pay into a workplace or private pension and you get 20% added in the form of Gov tax relief.

Let's say you retire at statute age and get the state pension. Let's say that the state amount is already pretty much at the lower rate tax allowance limit (£12570 atm).

Leaving any 25% tax free lump where it is, then you're going to be paying 20% income tax on any withdrawal that takes you over the lower rate. So basically, it's a zero sum game. I don't understand how the initial tax relief is of any benefit at all - other than maybe/hopefully earning some extra interest/earnings or whatever, which could increase the pot amount over time.

This all just seems a con to me. The gov are going to get their 20% back one way or another. Can someone explain - in simple terms?

EDIT: Ok, so you're only going to effectively get taxed once on income rather than twice. Hmm....is that it?......you're still going to get taxed though, so I still don't see the 'free gov money' thing.