Hello,  
Lawns that are thick and healthy do not need rolling, because the healthy root zone is not prone to winter heaving. If you have had extensive mole activity over a large area, rolling can be used to press the tunnels down. However, if moles are still present more tunnels will appear.

You are correct in thinking that soil compaction will result- so it is a trade-off: do you need a quick way to press mole tunnels down, or do you want soil that has a healthy amount of air spaces in the root zone?.

Here in Michigan the only rolling recommendations I can find in the research are for athletic fields and bent grass greens on golf courses- these techniques are for different types of grass, they have different levels of maintenance, and don’t apply to residential lawns.  

Here is an overview of Rolling from the University of Kentucky: “Rolling is not often considered a regular maintenance practice. In fact, rolling wet, heavy clay soils will cause soil compaction and decrease soil aeration. However, on well-drained, medium, and coarse-textured soils, rolling may help:
reduce desiccation in late winter or early spring by pressing frost-heaved plants back into the soil. This process most frequently benefits fall-seeded lawns (so roll the following spring) and sparse turf areas under shade trees.
 Well-established lawns are seldom damaged by heaving.
 Smooth a soil surface roughened by mole runs, earthworms, and night crawlers. However, rolling will not correct surface undulations caused by improper grading.  Firm a loose seedbed immediately after the seed is broadcast. Germination and seedling development are very poor in loose, droughty seedbeds.  
With good moisture, a heavy roller will help remove minor roughness in the soil surface. Water-ballast rollers can often be rented. These rollers have a hollow drum that can be filled with water. By increasing or decreasing the amount of water in the roller, you can adjust the weight to give a firm seedbed or smooth a surface. If the lawn is sloping, a small garden tractor may be necessary to pull the roller. Rolling is most beneficial when the soil is moist, not wet.” (end of U of Kentucky extract)  

And, here is another opinion from University of Missouri Extension- “Rolling is not desirable for smooth, uneven lawns. Surface compaction is common in many lawns, without adding to the problem by heavy rolling. Rolling moist soil causes maximum compaction — a fine way to build roadways but not soils for turf. When late winter freezing and thawing have resulted in “heaving” young plants out of the ground, or if mole activity is serious, rolling may be required and is acceptable. In such cases, roll soon after spring thaw when the soil surface is relatively dry, and use as light a roller as possible. Don’t roll more than is absolutely necessary.” (end of U of Missouri extract)    

Another consideration is soil type. If you have clay soil, recovery of the air spaces will be much slower- perhaps several years- after one rolling treatment. If you have sandy soil, the amount of compaction could be less. A soil test can tell you your soil type, along with pH, some nutrient content, organic content, and fertilizer recommendations If you haven’t had a soil test, you can purchase one from MSU at www.msusoiltest.com  

So, if you are satisfied with your lawn there is no benefit to rolling. If your lawn is very lumpy and you want to try and smooth it, rolling can help. You may need to aerate the lawn after it has been rolled in order to help get air into the root zone again. MSU has a nice ‘Home Lawns’ section on their Turf website which addresses all aspects of lawn care. www.turf.msu.edu

Caring for your lawn with the basics recommended at the MSU site above should give you a healthy, thick lawn- assuming your have 6 or more hours of full sun during the growing season.  Please write again if you have more questions. Thank you for using our service.