To answer your question "surely a cheeky offer is always worth it", then answer is NO.
We priced our 3 bed semi sensibly to sell. £225k. It needed a bit of updating but nothing major, but we wanted to move as we'd seen a house we liked. It was in a fab location. Not many houses up for sale.
It went on the market and we had quite a lot of viewings. This one couple offered £180k. Bearing in mind £225k was a very competitive price and already reflected the bits of work that needed doing... Their offer felt like a p*ss take and we didn't see them as serious buyers.
Two days later we accepted £220k from someone else as we liked the couple and they were in a good position to move. This first couple were furious, offered £221k then £225k and were really pissed off when we refused it. The EA told us they kept asking if the sale had fallen through!
As it happened the house we wanted sold a couple of days before we sold ours, so we ended up not having a house to buy. The couple buying it then upped their offer to £225k if we would move into rented, so we did.
So it doesn't ALWAYS pay to offer low. You need to do your homework first e.g. how long it's been on the market, what other properties have sold for.