I'm an old guy, and not that technically savvy, but judging from the music videos I've seen and heard lately recorded on the latest smartphones, seems to me that would be hard to beat. The video quality is excellent.
Personally, I don't have a smartphone. I have an old fashioned flip phone cell phone for making and receiving calls, and an occasional text.
The audio on the smartphones is not that bad either, but Sam is right, a good quality audio recorder will make a difference in the sound of the audio.
For years I used a basic digital mini camcorder with the built in mic on the recorder. The sound quality was not that good, but neither was my piano playing.
Now, I still use the older camcorder for the video, but I also use a ZOOM H4n stereo audio recorder and sync the two files (video and audio) when I make/edit the music video file with my video editing software. I mute the audio portion of the video file, and try to synchronize the ZOOM audio file with the video. Not an easy task to get the sync 100%, but I can get pretty close if I keep working with it.
Also, the placement of the ZOOM H4n recorder is important. If not placed correctly, it is not that much better than the audio recording on the camcorder.
Next time around, I'll probably get the ZOOM video/audio recorder combo. No syncing involved.
Also, if you post your music video on YouTube, there will still be some loss of quality in the process.