Plenty of people do this and almost all of them enjoy it. The two things worth understanding first are the money and the vehicle.
Why it costs more per person
A safari price is mostly a vehicle, a guide and a room, and only the room gets cheaper when there are two of you. One person in a Land Cruiser pays for the whole Land Cruiser, and the guide's fee and the park entry for the vehicle don't halve either. Then camps charge a single supplement on top, because a room sold to one person earns them less than the same room sold to two.
So a solo trip is meaningfully more per person than the same itinerary for a couple. That isn't a markup, it's arithmetic, and any quote should show you where it sits.
Ways to bring it down
Travel in the green season, when single supplements are often waived or reduced. Ask for camps that don't charge one, because some don't. Join a small-group departure, where you share a vehicle with other travellers on fixed dates and the per-person price drops a long way. Or shorten the trip and keep the private vehicle, which most solo travellers prefer to lengthening it and sharing.
What you get that couples don't
The front seat, all day, and a guide who is talking to you rather than to the car. You decide when to stop and for how long. If you want to spend three hours at one waterhole because the light is good, nobody sighs. Solo travellers often come back having seen more, because they were willing to be patient.
Is it comfortable socially?
Mostly yes. Camps are small and dinner is often communal, so you'll meet people whether you want to or not. If you'd rather eat alone, say so, and nobody minds. Tanzanians are sociable and your guide will be good company for a week.
Safety
Not materially different from travelling as a pair. You're with a guide all day and in a camp at night. The ordinary precautions in Arusha or Dar apply to everybody, and they're covered in is Tanzania safe. Solo women travel here constantly and the usual report is that it was easier than expected.
One practical thing
Tell someone at home your itinerary, and leave the camp names and the operator's number with them. Phone signal is patchy in the parks and a quiet week is normal, which is only worrying if nobody knew in advance.
Questions before you share a vehicle
How many people, and how many window seats? Six in a Land Cruiser means everyone has a window; seven does not. What's the age range and what kind of trip is it, since a photography group and a family holiday run very differently. And is the itinerary fixed? A shared departure that can't wait at a sighting is a cheaper trip for a reason.