12v device runs fine on 5v

I'm working on a project based around a remote controlled electrical outlet set.
The goal is to drive the remote control board using a trinket pro, using signals from other input devices.
The remote uses a 12v a23 battery. Measuring the voltage across a remote board, it reads 12.5v.
If I have to supply 12v to the remote, step down to 9v to another element, as well as 5v to the arduino, then wire up a dozen transistors to allow the 5v arduino to control 12 12v switches, things become too physically large for my use case.
I tried using 9v to power the remote. It worked, with no noticeable side effects. Then I got curious, I tried powering it with 5v. It worked as well.
First I thought range would suffer, but the switches respond to the remote across the entire house. You can also program outlets to certain remote buttons. I thought, surely this would mess up their ability to talk to one another.but it didn't, they still program fine.
Using 5v for the arduino and the remote will make everything very small and require almost no circuit logic, but I feel like it's just horribly sloppy work.
Should I just use 5v? Should I not? Thoughts?

Should I just use 5v? Should I not? Thoughts?

My thought is that if it does what you want on 5V then 5V is OK. It would be nice to know why 5V is OK, but I can't tell you that from the information provided, other than to provide a generic answer that maybe it was designed for anything between (at least) 5V to 12V.

First I thought range would suffer

There is a fair chance that range in fact did suffer - it could have gone from "way more than needed" to "just enough". In either case the receivers will pick up the signal.

Many circuits can accept a rather wide voltage range. Typical effects of a lower voltage include less range / lower speed / higher sensitivity to noise.

Understood. Thank you both for taking the time to respond. I'm going to move ahead with the 5v.

It would be good to know at what voltage it fails at, or if it would work at a voltage a bit lower than 5V. That way you'd know if there's voltage range left to allow for variables like component aging, temperature, power supply loading, drift, etc.

If you happen to have a shockley diode handy, you could test everything at about 4.7V. Or just a regular signal diode in series to test at about 4.3-4.4V.