LEDs will use essentially an infinite current. Then they burn themselves up and die. So, the current needs to be controlled in some fashion. More current = more light. Less current = less light. You are correct that you can control the LED current by either turning the current on/off in a strobe fashion or by adjusting the power supplied (which is difficult since the voltage used by the LED changes as it heats, so you need to control the current and not voltage to have a consistent light output).
You can put a capacitor and inductor on the strobed current to turn it into a fairly consistent output. Meaning the LED light itself does not need to strobe.
Typically you'd use an LED driver to have very precise control of the LED output. The problem is that LED drivers are expensive and don't work well with other light sources. 1) You don't want LED drivers in the light switch/socket since that prevents you from using other lightbulbs. Until the LEDs take over and kill off CFLs and incandescents, that limits marketshare. Or, 2) you put the expensive LED driver into the lightbulb itself. Which means every lighbulb you buy has to have complex circuitry that adds a lot to the price and are redundant if you have more than one bulb in a light fixture. This high cost of redundant electronics prevents LEDs from taking over the market. So, you have a chicken and the egg problem. LED lightbulbs can't be made cheap until they take over the market, and LEDs can't take over the market until they become cheap.
So, in general, the answer has been to 3) put crappy cheap electronics in the bulb, which either makes them non-dimmable or severely limits the dimmable range.