I can definitely relate to this. While I don't actually write lyrics/record any vocals myself, I work as a freelance voice actor in addition to the composing/mixing work I've (slowly) been taking on over the last few months. The recording anxiety can be very, very real indeed. Sometimes I can walk into my booth and record an audition or voiceover in one or two takes without a sweat, and other times, nerves or doubts get the better of me and I wind up spending an inordinate amount of time trying to record what typically amounts to no more than a minute to two of audio on average.
Just last week, for example, I actually landed my first VO gig that required a "natural" (very heavy air quotes here) commercial read. As in, the sort of promotional, energetic-sounding almost 'guy-next-door' (ha, don't know if that's the right way to describe it, but whatever) type of delivery. I've done a couple commercial VOs before, but both featured more exaggerated 'character' voices. One, for example, was a parody of sorts of the typical movie announcer voice. To put it bluntly -- this type of "natural" VO, generally speaking, is about 1,000,000 miles outside my typical comfort zone and doesn't feel "natural" at all. Literally the last thing I recorded for prior to this role was a gigantic, screaming skeleton. Before that? I believe it may have been some sort of super-gruff, exaggerated soldier guy for an animation.
Anyway, here's my point; it all boiled down to the fact that everything about this particular voiceover didn't really click for me. For comparison's sake, let's say that the script was akin to the blatant lyrics you mention as an example in the OP, because there are indeed certain components that voiceover work and sung vocals share, in one way or another. Because the script required that overly-enthusiastic sounding "natural" commercial VO and 'tighter', more controlled/fluid vocal inflections and a certain rhythm and sense of pacing throughout, I ended up spending a good 4-5 hours trying to hammer out what amounted to about 1 minute and 40 seconds of recorded audio.
Everything was throwing me off. The fact that I wasn't as confident in my ability to produce this type of VO, combined with the largely acoustically flat recording space, led to me picking apart every tiny little flaw in the delivery of every individual line, every individual inflection, every breath, pause, and so on and so forth. And with every retake, it seemed to get worse; my uncertainty would mount and get the better of me, and 'controlling' that sense of rhythm became a challenge -- my speech seemed to lose clarity, I seemed to generate more 'mouth noise' with every failed take (clicks, gum-smacking, etc)...you get the picture. I imagine recording vocals has many of the same challenges. All of these things just add up and make the process of recording a battle against the self, so to speak.
That might sound like an overly dramatic way of putting it, but that's the best way I can think of to describe it. Overall, I love being able to make money by doing VO, but just like most jobs, it has moments of absolute frustration/nerve-wracking anxiety...even when I'm doing it all from the comfort of my own home entirely by my lonesome. It still doesn't change the fact that when I step into my booth with the mic on, I become very conscious of the fact that I'm about to record things with my voice in very high detail that other people are paying me money to say.
I used to think that gaining more experience and taking on more paid gigs would chip away at that anxiety until I could record and send off auditions and finished VOs without a sweat, but...nope. There's always a nagging sensation that I could've done something differently/better. I feel it with my music, too. Honestly, though...I think this is really, reaaally common for creative types.
As with all things, practice makes perfect -- or at least, practice makes you better than you were a few days ago and slightly more confident in your abilities for at least a few more days until you feel the ol' familiar itch of "I can do better...!" and go back to the drawing board again -- and there's really no end-all-be-all solution to curing or working around this type of uncertainty/anxiety when it crops up.
I imagine that the majority of even the most revered performers, entertainers, and musicians have all felt this same pang of uncertainty frequently at just about every moment; from the genesis of their aspirations to the heights of their professional careers.
In a weird way, that thought is sometimes enough to ground me and push me to just do the damn thing -- be it a voiceover or a composition or whatever else I might be working on at the time.
TL;DR - Leelius said it best. There's always anxiety in creating something.