To start with, bigger isn't always better. While our tractor-mounted aerifier can cover a whole lot of ground, the clean performance and tighter hole spacing that the walking machines give us, is now preferred.
We often say that the actual aerification process is pretty fast and simple--it's the cleanup afterwards that takes time and effort. Once the aerification plugs have dried a bit, we separate the thatch and soil by using an old fairway mower which has verticut reels, and pulls a steel drag mat. On a hot, dry day, this is a dirty job.
We then follow behind with our core harvesters, which pick up the thatch.
Back in the day, the final cleanup was done by a tractor-mounted PTO blower. Once again, we found the bigger machine wasn't necessarily the best machine for the job. Today, we use up to 10 backpack blowers to do a final cleaning of the turf. This is really labor intensive (and yes, another dirty job), but allows us to have a very clean finished product.
Some courses keep a set of old mowing units for cutting post-aerification, which they may refer to as mud or dirt reels. Given our detailed cleanup, these are not necessary!