You did not indicate the type of visa that you will be applying for. There are Thai embassies and consulates that will control the process for applying for a visa. Then there will also be Honorary consulates that have been granted special authority by Thai law (other countries have honorary consulates also) to issue Thai visas and perform other special consular duties.
For single-entry Thai visas, it might be more efficient to use an honorary Thai consulate. There are several of them scattered throughout the USA, and most of them will accept applications via overnight mail. Honorary Thai consulates worldwide no longer issue multiple-entry visas of any category after August 2016. You must go (or in some cases mail) to the Thai embassy or a Thai consulate to obtain your visa. Or you can use a friend to drop off the visa application and pick it back up (basically doing what a visa runner agent would do). You shouldn't need a limited power of attorney, but it may not be a bad idea.
Or you can also use visa runner agents and such, but in a place like the USA I would check a few honorary consulates first like Dallas, TX or Portland, OR. I might use an agent in a place like Penang, Malaysia because the price is reasonable and you actually save 2 trips.