I echo what Guitarhacker is saying. I'm certainly no pro but no "copycat" either. Playing (or singing) songs on a chosen instrument (or your voice) from start to finish is also how I define a musician. If the song is a cover, then adding elements to make it your interpretation is also important.
In my opinion, if you record yourself and then in your DAW have to cut, paste, copy, snip, stretch, move, flip, chop or otherwise perform major surgury on your recording to get it to a listenable state, then you probably haven't learnt the song to begin with and you are functioning more as a computer operator than a muscian. If there is a magic short cut here, I'm unaware of it. For those of us that are not gifted prodigies it takes work, effort, repetiveness, motivation and time; in other words, a journey that you have to invest in. And for me there is more satisfaction in the 2-steps forward and 1-step backwards journey than the end result.
Everyone has their own personal motivation(s). For me it's about three things: 1) the thrill of the hunt (that is, the process of learning the new song), 2) the passion for music and 3) the sense of accomplishment in producing a body of work.
I think for most people starting out, it has to begin with goal setting.
Edit: Another point to be made is that with todays tools it has never been easier to learn to play songs. Decades ago, tools to slow down a track, transpose it or loop it didn't exist. I wouldn't be surprised that some on this forum are well-aquainted with dropping needles on vinyl day after day in order to learn the riff causing the needles and the vinyl to literally wear out. We should admire such folks.