You did not indicate the type of visa that you will be applying for. ThereThere are Thai Embassiesembassies and official Thai Consulatesconsulates that will control the process for applying for a visa. ThenThen there will also be Honorary consulates that have been granted special authority by Thai law (other countries have honorary consulates also) to issue thaiThai visas and perform other special consular duties.
For Single Entrysingle-entry Thai Visasvisas, 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-entry visas of any category after August, 2016. YouYou must go (or in some cases mail) to the Thai Embassyembassy or officiala Thai consulate to obtain your visa. OrOr 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). YouYou 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. II might use an agent in a place like Penang, Malaysia because the price is reasonable and you actually save 2 trips.