I would like to do it this way because I am a singer-songwriter and doing both at same time feels so much natural.
Thoughts?
There is a part of me that doesn't want to talk you out of doing what you intend. After all, it is the way you are most comfortable and too often on this and other forums, a person asks a question and many of the answers don't actually answer the question in a manner that is helpful to the questioner. Very often the answers are just attempts to dissuade the questioner from doing something that the answerer considers difficult or passé.
But it's only part of me that feels this way !
This is my logic, which is only offered up as a consideration.
Natural doesn't come into it. We are now a good 70+ years into multitrack recording. For the first 30~40 years of that period {from the late 40s until into the 80s} the overwhelming majority of artists of just about every genre known to man, beast and God developed their musicality in some kind of ensemble context. If we put aside the majority of those artists and just concentrate on those that played an instrument and sang, many of the greats from the early 60s onwards, who would have learned playing and singing simultaneously had to learn the rigours of studio recording. And that meant learning how to get the instruments down first, then getting the vocals down. It may not have been that much of a trial for those bands that had a dedicated singer but for those self contained units {your Beatles, Pink Floyds, Lovin' Spoonfuls, Status Quos etc} with singer/instrumentalists, they had to become comfortable with being able to do both the studio thing
and go out and do it live.
And didn't they all do a great job ? To the extent that finding that artist that records an instrument at the same time as recording their vocal in the studio is so much the exception that it's quite a story when one finds that person.
Even if you don't do it
now, I think it's a discipline that you should learn and utilize. I'm the same with clicks ~ I don't want to hear people saying they can't use them because if their family's life depended on it, they'd be able to !
Rather, my philosophy is that you should be able to record with a click ~ and you should be able to record without one.
Same with recording vocals as a singer/instrumentalist.