I would expect you only use one set of outputs at any one time

Thanks for the response Tony. I think I was hoping to eliminate the DI and simplify my stage setup.

Both outputs work at the same time on my CP4. For one band rehearsal setup, I send XLR outputs to the band mixer, and the 1/4" outputs to my small monitor speakers, which sit atop my keyboards. (I also plug my Nord Electro into the CP4's audio input. I love this feature and the fact that the CP4's master volume doesn't affect it.)

I tried this just now, and plugging and unplugging one output (or set of outputs, for stereo) has no noticeable effect on the volume of the other. I tried this with just Left channel (mono mode) and with both channels. I also tried the OP's situation, stereo XLR and mono 1/4" in Left jack. Same results with master volume at 1:00 or turned all the way up: no volume change in one type when plugging and unplugging the other type. I would probably have noticed a 1dB change, and definitely noticed a 3dB change.

You might still want a DI box. A DI box does these things:

1) convert 1/4" to XLR -- no need since CP4 has XLR outputs.
2) convert unbalanced to balanced -- no need since CP4's XLR outputs are balanced (as are the 1/4" outputs, I believe).
3) optional ground lift to avoid buzz -- CP4 has ground always lifted. IMHO this is the best case. I have occasionally got less buzz on a DI box with ground connected, but haven't ever had this need with the CP4 (knock on wood)
4) reduce signal strength from line level to mic levels -- sometimes required, though most mixers have pad and enough gain range (all the ones I've connected to have been OK)
5) convert hi-impedance to low impedance -- This used to be more important; back in the 70's and 80's it could damage a hi-Z output to connect it to a low-Z output. These days the worst outcome is distortion, but I haven't ever noticed any. Still, I bet the EE types would recommend impedance matching.
6) Isolates phantom power. I have no idea how CP4 responds to phantom power, but I wouldn't want to try it.

Impedance matching is very important for very weak signals like dynamic mic signals, since it maximizes the power transfer across the interface, which maximizes signal-to-noise ratio. Line levels are beefy enough that this isn't a concern. The only concern is that with low impedance loads, the line output has to push too much current to deliver the necessary output voltage. My guess is that with most gear today, mic inputs are higher impedance than they used to be, line outputs are beefier than they used to be, and it's all good.

So, a DI box is a good item to have in the kit, but might usually be unnecessary, adding it only in case of problems, or if you notice a degradation in audio quality.

In any case, you can always use the headphone outputs as a secondary line output. These days, headphone outputs are pretty much the same as line outputs, just beefed up a bit to handle lower impedance loads, and possibly with a bit more gain in case of inefficient headphones. They're compatible with line inputs; you just have to make sure they're not turned up too high (to distort the input circuitry).

Hmm... Thanks Jeff for all the info and detail.

I'm a bit concerned as my setup was the same as your rehearsal setup in your first paragraph (except the stereo 1/4" unbalanced output was only mono in my case).
Only other difference is the XLRs ran to a snake, then back to the house mixer in the theatre.
As soon as they plugged the XLRs into my CP4, the 1/4" L unbalanced output to my monitor dropped to virtually nothing and a bit of distortion.

I'm going to have to try a bit of testing in my living room tomorrow to confirm if there is a problem with my CP4 outputs.

Thanks again Jeff.

KJ

UPDATE: I just tested again and everything worked fine. I wonder if they house system had something funky going on that caused my 1/4" outputs to lose most of their signal. Not sure what would cause that though... phantom power maybe??
Regardless, piano is working as expected now!
Thanks

Yeah, I bet it's phantom power. I forgot to mention this as yet another thing a DI box handles, so I'll edit my post and add it.

I doubt it's impedance. As a quick test, I just played my CP4 while listening to 1/4" outs, and momentarily shorted the XLR pins. No audible effect at all. So, impedance issues at the other end can't be it.

If it is phantom power, a solution is an "isolator" such as the ART DTI (stereo isolator). It's like a DI box, except that it has XLR connectors on both sides, and it's "1:1" meaning that it doesn't change the impedance or signal level. Frankly, a better solution is a DI box with "thru" connectors, and use the 1/4" outputs.

Note that using stereo 1/4" sends to a stereo DI box, and using "thru" on just one channel, you lose the summing to mono feature. However, I find that the vast majority of patches sound better NOT summed to mono. I could go on for days about this, but it's better to try it yourself and choose what sounds best. There are counterexamples, of course: patches that do sound better summed to mono. None that I'm aware of on the CP4. In general, the right output is better, though you lose a bit of bass note volume on CP4 stereo pianos. The stereo panning on CP4 pianos is subtle enough that it's not a problem.

Whenever I play any keyboard in mono, I use the non-summed output (usually, the Right side).