It definitely comes down to consistency. A good house cue can be a great playing cue but finding one on a regular basis is a sketchy proposition in most places. If you do happen to be blessed with a place that has an ample supply of quality house cues in good shape you still may not get one that plays the same every time. Different tips, weights, etc all come into play.
Beyond that, a house cue is typically a very stiff taper, butt heavy design with a 13mm shaft and some of poorly maintained tip. That is far from my personal preference so while I can grab a house cue and play, it definitely doesn't feel the way I like my cues to feel (forward balance, linen wrapped, 12mm shaft). So it can also be important to have your own cue so you have one that fits you personal preferences.
While there are always anecdotal tails about people who prefer to play with a house cue, and I've even on occasion seen someone walk in with their own 1-piece cue they brought with them, there is a good reason the huge majority of players have their own 2-piece cue that they can easily carry around.
Now, if I mostly played on a home table I'd love to have a 1-piece cue setup to my preferences and see how one can really play when it matches what I like in a cue. They definitely have a great feeling hit and I'm sure it'd be awesome.