Will a higher recording quality provide better results or is CD quality more than enough?

I listen to MP3s or FLACs on my cell phone most of the time.  I also will occasionally listen to music online.  
I hardly play CDs anymore.  
Hell yes.

1 - Why would you accept a lower quality recording?
2 - A huge amount of people prefer to buy CDs.

Remember that while the market in some countries is greater for downloads that CDs, in others it is the other way around.  Couple that with the ongoing rebirth of vinyl (which many consider to have the highest quality of all formats) and you have no choice but to aim at the highest quality possible.

Why would the evolution of technology result in a reduction in quality?  That would be a backwards step.

Also, I think the OP in itself is flawed.  MP3s are very low quality compared to CD, whereas I believe FLAC is pretty much the same as & possibly better than CD (I'm not an expert here though).  If you use FLAC, CD quality is the minimum requirement.  

If you only want to record an MP3 for your own use, then a lower quality is acceptable but certainly shouldn't be the target.  Any product intended to be marketed should be the highest possible quality.
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Mp3's are OK for walking around and playing on cell phones, mp3 players, etc. because they take up so much less space on a flash drive (hard drive etc.) and the general outside noises make critical listening impossible.  The compression ratios on an mp3 file can be extreme as they eliminate actual frequencies above and below the normal hearing range. Many people believe that those upper and lower frequencies that are removed in order to shrink and compress the file size on an mp3 file have an effect on the overall sound. FLAC, ALAC and WAV can be better technically than CD quality though depending on your listening environment and playback media it many not be even slightly noticeable. It all depends on what you are listening to your music on. If you are using inexpensive ear buds or lower quality headphones you probably won't hear any difference between mp3, FLAC, ALAC,WAV or CD but in the pro or semi pro studio environment mp3 is not anything close to high quality and is not (or shouldn't be) used except as a low quality product to upload to a web site or email. It's convenient, and it's accepted by the general public as a standard but it's not good quality.  

It might help to think of audio compression files like the mega pixels on a digital camera. Back in 2000 I bought my first digital camera a Kodak DC280 that took pictures in a 2 mega pixel format. It was really great at the time and cost just over $500. As years and technology progressed cameras have increased dramatically to much higher mega pixel rates. If I compare my 2.0 Kodak to the 16 mega pixel  camera in my phone, there is a huge difference in clarity and quality. You might say my 2 mega pixel camera was like an mp3 compared to my cell phone camera which is more like a CD, FLAC etc. More detailed and clear.
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Last edited by Rickholly74 at Sep 21, 2017,
Well, there are some new technologies that are trying to emerge, supporting higher than 16bit/44.1khz as the final format, but nothing has taken serious hold. 
For the most part, mastering is for CD, which is higher quality than the lossy formats. There are some companies that master music differently, depending on the format to optimize the sound for whatever is needed...kinda like analog mastering for vinyl is different, due to the bass limitations of the medium, so is the different kinds of mp3 and other lossy formats.
A non-technical explanation of the OP's mentioned formats:

MP3 revolutionized the way we listen to music. Download small files and play on the go. Quality? Sub par. It's compressed, meaning there are lost frequencies from the mix.

FLAC is amazing. If your portable device can store it and you have a source from which to download, it is awesome. However, most $20 headphones/OEM cell phone headphones will not be able to play it back well enough to notice much difference.

CD quality is standard and amazing (as mentioned in previous posts). I prefer to pop the CD in my car, whether it be 311's new album, Mosaic, or Prophets of Rage's self titled, I'd rather listen to the CD than via Bluetooth or 3.5mm jack from Spotify on my Google Pixel.

My own takeaway: do not record at a level to which you wouldn't want to listen. Also, take in consideration the fact that you may want others to listen as well.
First, you shouldn't be recording at CD quality, which is 16 bit. You should record at 24 bit, which is probably the default in your daw. Never record at 16 bit.

Second, 24 bit 44.1k is fine . From that you can mixdown mp3's, wav files, etc. And things will sound great. You can mixdown 16 bit 44.1k from a 24 bit project in any daw, so you can still make a cd.

Third, mp3's actually sound fine now, as long as they are 320kbps.
320kbps mp3 still loses quite a bit of information, I've had cases where low end gets clouded or some slight extra fizz is added...in other words you can't trust the mp3 process to be your final mastered best quality file, so here I'll disagree with reverb66

16bit recording lowers the headroom quite a bit so it is better to record at 24bit, but you can listen to some albums done on 16bit where it doesn't really matter that much, especially on a rock record. Scorpions have recorded some of their biggest sellers from the 80s ("Blackout" being one) on a digital multitrack tape, which at the time was 16bit/44.1. Megadeth "Symphony..." was recorded on ADAT tape if not mistaken, 16/44 as well, so it could be done when you know what you're doing. In general it is best to record at 24bit, unless you can't at which point just record at 16/44, it is not so catastrophic as some people make it out to be.
Quote by diabolical
320kbps mp3 still loses quite a bit of information, I've had cases where low end gets clouded or some slight extra fizz is added...in other words you can't trust the mp3 process to be your final mastered best quality file, so here I'll disagree with reverb66. 

To be clear, I wasn't suggesting he use an mp3 as his Master - his "master" should be a 24 bit Wav. file - I was just stating that mp3s sound very good now compared to what they used to be.