Lawn care is expensive and time consuming. Why would you do this for a house you do not own?

Save the money and put it into your new home.

Coupe I won't doubt your numbers but won't verify. But you forgot the cost of time in your math. All the maintenance you describe, if done by the renter, costs time.

And time can be very valuable if wasted on a rent house.

OP thin the trees in the front or don't bother. Set up the back yard enough to have a BBQ with friends.

What kind of quality slow release fertilizer are you getting for $76 per year and how many times are you fertilizing?

It's pointless putting money into a lawn you don't own, period.

Time certainly is important, so let's look at it.

Mowing is going to take the most time. At the height of summer, I spend around 1 hour every 4 days mowing my 6000 sq ft with a push mower and 15 minutes weed eating. There are times it's a chore that takes away but if I schedule it correctly, it's an enjoyable task that allows me to get outside, get some sun, and listen to entertainment during times my family is otherwise ocupied. In total, I probably spend 50-60 hours mowing and weed eating a year. I could extend my mowing interval to once a week if I had to and get it down to 35-45 hours or so. But I still have to mow according to my HOA and if a rental, my landlord so let's call it 30 hours of extra mowing/weedeating.

The next longest task is the aeration which takes less 4 hours including pick up and drop off. Each chemical application takes 30 minutes. So 2 hours for fertilizer, 2 hours for antifungals, 1.5 for preemergents. The peat moss takes 1 hour. Add in 2 hours to go to the store plus 1.5 to make the math easier and for miscellaneous. That plus mowing puts me at 44 hours more than necessary.

But I enjoy the work, kids and dogs can play outside without tracking in mud, we can have picnics with the neighbors and their kids, the waterslide can be set up for 24+ hours every weekend without ruing the lawn or popping the slide, my family and I can lay in the grass comfortably, the house looks better, and, and, and. OP likely won't spend enough time in the rental to get his lawn up to the level of mine, but it'll get significantly better and he'll be able to enjoy it.

Maybe he looks at my numbers and decides it's not worth it. Maybe it is. Who knows? But it's not necessarily a waste even if the house is a rental.

I buy from Producer's Coop. I haven't had to in a while because their bags last me so long, so I can't give up to date pricing but I want to say it was around $40 a bag. I fertilize with a quick release around March, again with a slow release in April and July, and a winterizer in October. I probably use a bag each of the quick release and winterizer every 3 years and a bag of the slow release every 1-1.5 years.