Is it bad practice to always have a MOSFET on?

No, it is not necessarily bad practice to have a MOSFET always on. They are frequently used as power switches.

Since you only have N-channel MOSFETs, you probably want to do it something like this:

^{simulate this circuit – Schematic created using CircuitLab}

This is called low-side switching. You have done that properly with your two elements, but you need to move your main switch to the low side as well. This way your signal inputs are ground referenced. If the sources of your MOSFETs are not at ground you won't be able to activate the gate properly, because how 'on' a MOSFET is depends on the gate to source voltage.

SIG1 turns the whole thing on and off, while SIG2 and SIG3 control the individual segments.

You also will want pull-downs on the gates so they turn off reliably.

Make sure you use logic-level MOSFETs that will be fully turned on by 3.3V (don't use the threshold voltage for this).

Here's the problem: -

You need a PNP BJT or a P channel MOSFET to adequately switch on or off the 12 volt rail. And, whatever transistor you choose, you'll need a ground referenced transistor to activate the top-side transistor because you can't use a 3.3 volt logic signal on a transistor connected to 12 volts.

Apart from that you need gate pull-down resistors of circa 100 kΩ to 1 MΩ.

Assuming the heat dissipation is within spec, is it generally "acceptable" to have a mosfet on this long?

There is no reason not to have a MOSFET on forever, provided it's within heat limits.