Absolutely. Regular mail through the US Postal Service works just fine and there is nothing wrong with doing it that way. A stamp, an envelope, paper, and a pen are all you need.
InmateAid's letter service is an option, not a requirement. The reasons people use it come down to convenience and privacy. You can send a letter from your phone in minutes without gathering supplies, printing photos, or making a trip to a mailbox. The return address on everything that goes into the facility is InmateAid's Florida office, not your home address, which keeps your personal information out of the facility environment. And when you factor in the cost of stamps, envelopes, and paper, the per-letter price through InmateAid is comparable.
But if you have the time and the supplies and you do not have concerns about privacy, mailing letters yourself is perfectly fine. The inmate receives it the same way either way. Use whichever method works best for your situation.