Chronotype has a strong genetic component. If getting out of bed at the crack of dawn or before is torture, and if your brain is fogged until the sun has been up for a while, getting up in the morning to write is not feasible.
One caveat about the above - if you'd asked me a few years ago if I was a morning or a night person, I'd've said without hesitation that I was a night person and what you describe above is exactly how I felt about mornings. However, I have seasonal affective disorder and since being diagnosed and treated with therapy lamps, I turned into a morning person near enough overnight.
If someone's a night person and totally happy, there's no reason to worry about this. But if someone's a night person and also prone to depression or even just feeling generally crap and never fully awake especially during winter, the genetic difference may actually be a predisposition towards seasonal affective disorder.
Being not fully awake until the afternoon (or never waking up fully) is a symptom of SAD because your body's not getting the light it needs to properly wake up and regulate your melatonin, body clock, etc. The first signs I get of SAD is feeling not properly awake and this feeling can last until the afternoon or last all day and gradually gets worse each day. From there it's a slow descent into depression over a period of weeks. I only was aware that this was the first signs of SAD after being diagnosed. Before, I just kind of accepted that I wasn't a morning person.
SAD isn't on many doctors radars and is commonly misdiagnosed as other mental health issues. The seasonal nature of it isn't always obvious. I haven't suffered from diagnosable clinical depression every single winter. In a lot of years it didn't get bad enough to see a doctor, when it did being fine again by May was put down to the antidepressants working, not the weather. This year I haven't had to use the therapy lamp on that many mornings even though it's already November because summer weather lasted until mid October and since then although it's been cold it's unseasonably bright and we haven't had much rain - other years there may be days and days of cloud and rain so there'll be much less light. Other stress can make the difference between constantly feeling tired and just generally dull, and actual clinical depression. Some degree of feeling crap in winter and crap on rainy days is accepted as normal, so it's hard to know given that we all only have experience of being ourselves, what the difference is between normal "aww, it's raining" feeling dull and the early signs of SAD.
Anyway, that's certainly not to say that everyone who's not a morning person has SAD, I'm just putting the info out there in case it helps anyone now or in the future.