I may side with your wife on this one, sorry. I think if I only had 1 acre to tend to a ZTR Toro from Home Depot would be on my list and maybe a snow blower as opposed to a tractor. The ZTR is much more adapt to mowing. However, the tractor is waaaaaaaaaaaaaaay more fun. The ZTR is a blast too.
I have to say that if ALL you are doing is mowing grass, a lawnmower is all you need. They are the best thing you can get for that chore as that is ALL that they are designed for. IF you need to do other things like remove snow, move dirt or other material, dig ditches or stumps or rocks out(backhoe required) grade gravel driveway etc, just to name a few chores that a tractor can do then a lawn mower is not your best tool. Granted one can rent a tractor when needed for a specific function, but there is nothing like having one setting on your property and ready to work when needed.
As for myself, I never even considered using one of my tractors for mowing, I have ZTR mowers for that and they are much better and faster than a tractor could do the job due to all the obstacles I have like trees, bushes, lawn ornaments etc. that have to mow around. I use the tractors for tractor work, like digging and hauling. Not everyone can afford several motorized implements though and a tractor that can do all of the chores although not as efficiently as a dedicated ZTR would still be much cheaper than buying a ATV like Polaris, Kubota RTV etc($10-15K) to haul materials, a snow blower to clear driveway (?$2K never priced them), ZTR to mow with ($3-10K depending on size and quality) and you still wouldn't have anything to grade and smooth a driveway with, dig up rocks, stumps etc, load and move pallets of material, lift heavy objects to save the back, till up a garden(forgot to add tiller to your powered tools ($1500)
So lets add up, tiller $1500, ZTR mid range $8,000, Utility vehicle $10,000 minimum used possibly, snow blower $2,000. That looks like over $21K to me and doesn't do all the things a tractor and implements of same price would do.
Sure you can GET BY with a 26" push mower and a couple of shovels, and a soil spade/ tined thingy for tilling but who wants to or has the kind of time it would take to mow even a half acre with a push mower, till a garden with a spade,etc.