Hope you don't me adding my 2p worth but as a mum who's only ever held a couple of parties (my son's now 15!), thought I'd explain why .....
.... as a single mum from when he was 4 till when he was 13, I did find the extra expense a worry, but agree, it can be done cheaply. However, more than that, it was the organisation of such events - especially when he was younger - that put me off as it was me on my own with no extra hands to help. I always worked fulltime and therefore had very little opportunity to get to know most of the other mums, therefore, a party, would have been, for me a bit of a logistical nightmare.
As he got older, I'd take son and 2 or 3 friends out, but wouldn't have wanted a housefull of kids on my own.
Yes - my son did go to others' parties - but not that many over the years and I'm sure this had more to do with the fact that I wasn't friendly (not through choice) with the other mums than anything. When he did go, I always ensured the child in question was bought a decent gift, which, I think should be reciprocation enough for the invite. Additionally, on rare days off, my son would invite friends back for tea etc.
I would have liked more parties - for my son's sake - but for some people it's simply not possible, and for some poor unfortunates even a "cheap" party is an extra expense which means delaying paying the gas bill ! Guess that other families can also be restricted by where they live, or by 1 or other parent's fear of social gatherings.
Certainly, when I did have parties (or do days out), I didn't log which kids returned the favour. It wasn't about me feeling my hospitality as an adult was returned, it was about what my son wanted on his birthday - and if that meant inviting a child who never had parties then so be it.