You've just described a constant current regulator.
A true constant current regulator would be what we call a "buck/boost driver." We will all "get on the same page" eventually. Nobody panic! :)
I'm not exactly certain what effects manufacturing tolerances will have on 3 ganged bucks (a single 3A one would be far better!) but it might be as well to start by ganging just 2 and check nothing overheats before adding the third.
The new crop of some leds supposedly can run overdriven at 2.8A (each.) 2x1A bucks should be fine if we are talking of driving a single recent-high-tech led. This is a different story if the hypothetical experimentor is attempting to run 2 or more LED in parallel. I'm basically agreeing that 2x1a buck to feed one led COULD work, depending on a few things.
If we're talking about running a parallel-wired triple star of some recent leds, 3x1a bucks WITHOUT PULSE MODULATION should work. A lot of these stars are only "advertised" running at 100-500 mA, though.
This can easily get confusing and complicated, particularly if we are all talking about different components. The simplicity of one proper driver to one proper led is kind of nice. Some drivers support multiple output options, which is also nice.
A driver that uses PWM (pulse width modulation) would probably act really strangely when used in a gang to drive one LED.
Don't think of a LED as a "resistor" with a constant resistance. It's actually a
reactive component, with its electrical properties changing based on its drive at a particular instant and even temperature and such.
Short version: When you feed several simultaneous waveforms (pulse width modulation) to a single LED, the math gets REALLY WEIRD. It's because an LED is "dynamically reactive" and not "uniformly resistive." You can't really say that an LED is "3.7V." That wouldn't be accurate.
Right? Let's have some questions. If I've said anything wrong, standard disclaimer: jump in and let's hear it.