With respect, I think the reason you think that way is because you have never had a properly functioning HVAC system. I promise you that the many thousands of brilliant scientists and engineers that have worked on the science of psychrometrics have not made a mistake in designing HVAC systems to run continuously.
The most likely reason that you have a distorted view of a continuously-operating HVAC system is because for the last 2+ decades you have lived in a home that has about 3x too much AC capacity for the vast majority of days (not your fault). When the AC kicks on it is blasting you with arctic chilled air blowing with 3x the velocity ("wind") that it should. The air coming from the registers in a properly sized system will be far closer to the ambient temperature and you won't notice it being "freezing", nor will you notice it blowing on you because it will move much more slowly. If you are freezing with the thermostat set to 78F, then putting in another oversized system (2 ton) will continue to give you comfort problems, albeit not as much as a 3 ton system.
A properly sized and designed system will be invisible. You should not notice it being on at all. No hot spots nor cold spots in the home, and no noticeable air blowing on you. That all requires that it runs as much as possible. That means luke warm air (in the winter) and slightly chilled air (in the summer) moving very slowly and not blowing directly onto humans. The proper difference in temperature from air going into the return and the air coming out of the registers (known as delta-T) should be only 20F. If you were able to measure the air in your current system I'm confident you would find the delta-T is much higher than that. That's why you are freezing your a** off when the system is turned on.
With a continuously running system, your comfort inside your home is tempered by radiation and conduction from the stuff inside it (walls, floor, ceiling, furniture, etc), not by convection via hot or cold air being blasted directly onto your skin. In other words, what keeps you optimally comfortable is that *everything* in your home is the same temperature (78F for example), not just the air inside the home. Here's a good building science blog post on the topic:
Don’t you just love to strip down to your socks and jump on the bed? As a kid, you may not get away with it, but you’re a grown man or woman now, so who’s to stop you? And then,…
www.energyvanguard.com
When you turn on an oversized system, the air temperature feels too hot or too cold very quickly. That's why you turn it off - its uncomforable. Meanwhile, everything else in your home (building materials, furniture, etc) remains too warm (in the summer) or too cold (in the winter). Air is a poor conductor of heat energy. It takes lots of time for the air coming out of the registers to turn the entire building and contents into a consistent temperature. A proper-sized system will run as much as possible so that the entire building structure reaches nearly the same temperature. That's comfortable because it is invisible to you.
BTW, mini splits use compressors with inverters. That means that a single unit's capacity is not one value (e.g., 1 ton). Instead, the compressor is able to vary from the nameplate rating (e.g., 12K / 1 ton) to a very low capacity (e.g., 2.5K or just 1/5 ton). They are designed to run constantly. They do so by only producing enough heat or cold to maintain your setpoint (e.g., 78F). That means the under normal conditions, the air coming out of them should feel almost the same as the ambient room air if you put your hand in front of the blower.
In contrast, central systems rarely use inverters (although they are available but expensive). Central systems are usually single-stage, and I'm sure that's what has been quoted to you. That means the system is either totally on (100%) or off (0%). That's not great, but if you right-size the system, most days it will have long run times and keep you very comfortable. A good compromise is a 2-stage central system which runs at about 70% of capacity when it first turns on, and then ramps up to 100% if needed. I have a 2-stage system. This allows it to run more often in the "shoulder seasons" of fall and spring. That allows it to dehumidify well even when it isn't blazing hot out in the middle of summer. My 2-stage system runs in the first stage (70% capacity) about 90% of the time. It only ramps up to 100% capacity on the very hottest hours of the very hottest days.
Your last response makes it sound like you might not want want evidence-based advice, so I guess I'll stop bothering you with my time and effort. I guess that might have been why PoorUB stopped posting. I was trying to return the favor done to me from the brilliant people that have posted about HVAC on forums that I've learned from.