I have explored a dehumidifier for my Florida home, and after looking at the numbers, it just made more sense to tighten up the envelope and set the AC to 74. I have solar on the roof though, so the energy costs aren’t terribly high (vs possible mold remediation) for this approach. YMMV.
It operates a compressor that condenses a fluid with a boiling point below room temperature. As it condenses to a liquid, it generates a lot of heat. This heat is removed from the liquid. The liquid is then allowed to boil, which pulls heat from the environment.
In an air conditioner, the heat is radiated outside, and the cool air is vented inside. In a dehumidifier, the air is sucked in, blown over the cool radiator, which creates condensation which is collected, then blown over the hot radiator, and then blown back into the house.
So you might as well just use an AC and be more comfortable. There aren't any upsides to using a dehumidifier.
Both air conditioners and dehumidifiers are built on heat pumps. They both dehumidify in the same way: water condenses on a coil and drains away. But an AC unit pumps the extracted heat outside, and a dehumidifier pumps it back inside. When it's hot and humid, it wouldn't make sense to forgo the opportunity to pump heat outside.
A better solution is to get some variation of a two-stage air conditioner. Instead of a compressor that's either off or on, these have a compressor that can run at two speeds. Most of the time, it runs at the lower speed and behaves like an AC that is undersized, runs longer, and dehumidifies well. But when it gets really hot, it goes up to full speed so it can the temperature down. Compared to a single-stage AC, it costs more, but it's more energy-efficient and quieter and more comfortable because of smaller temperature swings.
These days they also variable-speed air conditioners that can adjust in tiny increments and run the compressor at almost any speed, so they are kind of the next generation beyond two-stage. They more or less run continuously, adjusting their power level instead of having an on/off duty cycle. It costs more than a two-stage, but it is even more efficient, quieter, and comfortable.
However, some of those other variables are not consistent across different designs. For example, they may use a different refrigerant that requires a different compressor. Centrifugal devices like fans and compressors use power in a non-linear fashion. Look up pychrometric chart and/or fan affinity laws for more detail
(Yes, I'm aware that such a set-up would be impractically noisy; it's just a thought experiment.)
An air conditioner has its heat pump capacity sized to cool a house, far in excess of what is needed merely to remove the humidity.
Generally most modern forced air systems are designed to run more often (for heat and cool) / longer periods of time now.
On top of that you can get multi stage AC units. Mine will run at a lower setting for a longer period of time when the less efficient "full blast" stage is too much, but AC is still needed.
If you live somewhere that humidity is an issue - in some places that's in the winter (when you wouldn't use cooling AC) - get a whole house dehumidifier system. Ex: https://www.sylvane.com/whole-house-dehumidifiers.html -- Those will run and maintain the correct humidity regardless of AC.
Use the right tool for the right and you'll get the most efficient results.
They have compressors which can adjust speed, not just turn off/on like a single-stage AC compressor does. So there's a lot less worry about whether it's sized right because it basically "resizes" itself as necessary.
The two-stage type has off/low/high, so it can get a lot closer to the right size. The variable-speed type is essentially continuously adjustable, so it's like always having the perfectly-sized AC unit for whatever the weather happens to be like today.
From my 96 year old grandfather: We planned to replace every piece of plaster in the wall in 10 years, and we kept hardwood floors because we could throw the rugs away and sand the floors down when the mold started to get bad.
That's wasteful and time intensive. No thanks.
Essential? You mean these climates were completely uninhabited before the invention of AC?