Not at all; you are deciding whether or not to invest smaller lump sums over and over. The comparison to a large lump sum is completely apt, the scale is simply different.
Recently, for example, you would have been sitting on cash since 2011 (last time there was a 10% drop) with it literally earning nothing. In the meantime the S&P has almost doubled, so you'd need a ~50% crash just to buy in at that level again. And that's not including the dividends you missed out on in the meantime!
Again, some basic googling will give you lots of academic studies about this. It's market timing. It doesn't work unless you get very lucky or have a crystal ball. There are very long periods where the market doesn't dip 10% at all. There are also crashes where the first 10% is just the beginning of a long downturn. In the meantime, of course, your cash is losing value, whether you have a little of it or a lot.
It's not controversial. It doesn't work.
-W
The problem with that comparison is that it defies reality: most people do not have to choose between the option of investing a large sum once and then leaving it never to invest again or holding it for regular purchases during dips. For the average investor, the real scenario is deciding whether they should set up automatic investments on payday or hold those savings for a few weeks/months until the market "dips" to invest in bulk, then continuously repeat the process. That's the scenario that needs to be run for this to be an effective case study.