I disagree. Pricing by the lot size up to 20 -25K sq ft is the best way to do it. How far off can you really be? Just have specific addons for obvious time consumers like corner lots, fences, pools, etc.
Above 25K I would want to look at the lawn before I give a price but even then you need to have a system in place to price it. How long does it take to trim around a tree? How many trees? Price per foot for blade edging? Price per foot for trimming along fences? One side or both sides? What size mower can be used? Etc, etc.
Eyeballing can work if you never plan to get out of a very hands on role in your company. But put together a detailed pricing system and then it doesn't matter who goes to do the pricing, you'll come up with the same price either way.