This is something I asked myself and I'd read others question this online too. Recently I had someone privately messaged me to ask my thoughts on it so I figured I'd throw my thoughts out there, for what it's worth.
For me, hairdressing was a passion that I've wanted to explore for the past twelve or so years. Back then I didn't think I would ever be in this industry, I figured I was just set to be an office/call centre worker and that was that. I did, however cut my mums hair for her on a regular basis. She wore it in a pixie style cut and I know I did a great job considering I had no qualifications and You Tube certainly wasn't around to watch "how to" videos. She was always happy with it and I had fun doing it. Actually, I used to cut layers in my own hair too now that I think of it and they did look great!
When I started on You Tube, people said that I should do a nail course. I did at that time consider doing hairdressing instead but I knew that ultimately, nails was what I wanted to pursue first. It seemed like a natural step to then go ahead and do beauty and after two years in college, I was ready for a little break from the routine of college on certain nights a week etc. As I knew hairdressing required two nights a week, I did a short pre-blended aromatherapy course which literally bored me to tears, I'm not going to lie (but I completed it!) rather than nothing for the year and then I finally took the plunge to enrol for hairdressing.
I think to answer the question it depends on your circumstances. If you have a huge client base of nail or beauty clients then you have to ask yourself how much time you will ultimately have, free for hairdressing services too. If you currently have the free time then I think it can only be a bonus, your existing clients can have their hair done at the same time so there is no need to search for separate people to do the job. Another point is if you were a mobile hairdresser only for example, then of course you just have to stand around whilst the hair colour develops but if you have other skills your client may actually book you for nails or something else that you do while you wait. To me it just gives potential clients more choice to choose your services, the more you do the more likely it is that you'll gain clients.
On the flip side, a major downfall is that there is only one of you (which is obvious but hopefully you get what I'm saying!) Whilst it's brilliant to be booked for a wedding or event, there is only a certain amount of jobs that can be done by one person so you'd need to be incredibly organised and know your limit. Of course if you're confident in some hairdressing/beauty friends you could enlist them to do large groups with you.
So to sum up, can you do both? Of course you can!! They're both big skills to learn but if you've got one down and you have the time and passion to learn the other, why not?!