Well this is simply not entirely true, may be for an android user but not for iPhone user for sure.
You can certainly record a great video covers with your mobile phone with great video and audio, relatively easy and cheap. It’s ranging from cheap (less than $50) and some effort to easy for about $110.
Cheap is using entry level audio interface with 1/4” instrument connection and record into sd card and doing the editing in either GarageBand or iMovie both are free.
Another is to get something like a Roland GoMixer Pro or JoYo MoMix pro and connect your phone and press record and you are done. The audio track is coming from your phone and it’s recording direct to your video.
JOYO Audio Mixer USB Audio Interface Stereo XLR+48V Phantom Power Mixer for Live Streaming Recording Podcasting Plug & Play (MOMIX PRO) Amazon.com
Here are a few example of the Roland GoMixer Pro and JoYo MoMix Pro they are pretty much the same, as I use the Roland 4camera app on my iPhone 12 Pro Max. I finished it up on my iMovie app on my iphone and iPad (I can’t see iPhone small screen very well, 
). Dunno ‘bout you guys but listening to it now I still think that it sounds ok.
I just edited this first one since it’s the same song and both basses are short scale.
@Blaze PM me if you have any questions. I’ll also post another link explaining the interface later.