I have two rentals - a duplex and a SFR
At the duplex, I price the cost of lawn maintenance in. I pay a service to mow the lawn, once every other week. I'ts usually all the tenants want, to have a lawn that looks maintained and not have to maintain it. The house fits in with others on the block in most cases.
The SFR mows her own lawn, and is bound by city ordinance per the lease.
I am not a lawn freak, however if either of them get to the point where they affect others, i.e. the neighbors that already have my number calling me - or the city code enforcement - we will have a problem. On the flip side, if the tenants, neighbors, and city are happy - I will not make it my business to interfere. If worse comes to worse, there is a lease clause in the SFR stating that they will maintain the lawn and if the city cites them, all expenses including my expenses to enforce the lease in court are their obligation. My bi-weekly lawncare schedule fits with the neighborhood norms on the duplex and the tenants tell me the property looks good to them.
My philosophy is - who am I to enforce my own aesthetic values on the folks who are intimately involved in the day-to-day use of the property? Especially in the case of an overgrown lawn that can be easily be double-mowed and brought back into compliance in the case of tenant neglect? These are really the least of my worries as long as all other obligations are being upheld.
Right now, I have 3 stellar tenants who pay early and via direct deposit, I try to treat them well and give them incentive to stay. If they asked for the lawn to be cut weekly for them, I would absolutely offer to have the service performed for them and build the extra costs into their monthly rent if it means the difference between them staying long term or moving somewhere where they could be happier.
I would find a win-win for both of you, and not expect the tenants to maintain the lawn to the level that you might at your own home.