IMHO, the only place for a pair of pull-ons is as a supplement to your lace-ups (if you do any real outdoors work). As stated, ankle support is crucial in many tasks required of boots, pull-ons don't have ankle support.
Yet, there are times when the pull-ons would be a great convenience item.
Therefore, I believe that if you must have pull-ons, it should only be after you have a good pair of lace-ups.
For me, I don't see much benefit to having the convenience of the pull-ons, but for others I could see it. I have been wearing lace-up Redwings for about 20 years now. I'm only on my 3rd pair (just got them). I've had a few previous pairs re-soled a couple times, but the boot itself just keeps going...
I have pull on wellingtons for working around the house and out in the yard. I have lace up Timberland Pro's for working on and around machines in plants.
Lace up for me, better ankle support, I do underground utility work so they help keep dirt and crud out.
Rocky, Wolverine's,Carolina's all have been good to me.
I wore pull on cowboy boots all through high school. I loved them. Then I was diagnosed with fallen arches and they gave me custom orthotics which don't do well in boots loose enough to slip in and out of. I bought a pair of Bates side zip boots and loved them. They wore out and now I have a pair of Wolverine lace-ups. The side zips are great and fast on and off while still offering ankle support. I like these Wolverines but I may go back to side zips when I make my next annual boot purchase in April.