Maybe, but usually not. House lights have several disadvantages.
First and most importantly, the light from a flash is significantly brighter for its short duration. This allows you to use lower, less-noisy ISO settings and narrower apertures. The short burst of the flash pulse itself can also freeze motion better than a shutter, which is nice for sharpness.
In order to get the same level of output from an incandescent or fluorescent bulb, you'll need a lot of power — more than normal house lights, so you're in to making (or buying) a special setup of some sort. And if you're doing that, there are many special setups you can do using a flash as well.
That power, in turn, can be very hot, if you're using incandescent lights, which is not so good for your subject. Alternately, if you're using fluorescent tubes, you may have unpleasant color rendering issues to deal with. And the bright, constant light can make people's eyes contract so the pupils are tiny spots, which isn't what one always wants.
Sometimes, when you're going for a naturalistic, documentary look, artificial light can be a deal-breaker. But for many shots, it's very beneficial to modify the light in some way, even with just a reflector. Having a constant source of light makes it easier to see in advance how the light falls (and reflects) without taking test shots (or using the "model light" strobe feature of some flashes).
But, mostly, what you want to do is:
- Get your flash off-camera — ideally wirelessly. (Or, at least bounce it if you can't do that.)
- Get some basic light modifiers like an umbrella or softbox. They can be a bit clunky but are not really very expensive, and done right they will contribute to the look of the scene rather than stealing from it.
You should also experiment with balancing the flash output with the light that's already there — artificial indoor light or sunlight. That gives you a lot of creative control.