Correct, AU DRPs are based on whole shares only in my experience.
You have a valid point about the mathematical problem with DRPs and whole shares. For example, with my recent RIO dividend, I got 6 new shares, and have about $50 sitting there doing nothing until the next dividend.
Despite this, I still use DRPs for two reasons:
1. Behaviour. I know myself well enough to know that out of sight is out of mind. If I see the dollars come in as income, I then have to make a choice to reinvest. If I don't ever see the dollars, I don't have to deal with temptation. I'm increasingly of the view that avoiding behaviour is one of the tricks to good long term investing, and this helps.
2. DRP discounts. Some companies offer a discount on their DRP shares (0-5%). That's a bonus you wouldn't get if buying with the cash. An extra fraction of a percent on the DRP shares balances out any loss of earnings from money not reinvested pretty quickly.