A wise project manager once told me, the whole point of project management is to "get it done". If you're already finishing your project on time, on schedule, and on scope, then you are doing a good job, and your stakeholders are satisfied with you.
As for your project team, even if they (apparently) hate you, they seem to be working well with you (and that's why you are finishing your projects on time). So, in my opinion, don't switch personality to another (faked) one that you think might resonate better with your project team (I think if you do this you will confuse them and you will lose some - if not all - of their respect).
I have personally seen both ends of the spectrum and I think that project managers with soft skills are rewarded with a higher productivity. However, that doesn't mean that authoritarian project managers are bad, as most of them do a good job (you are a perfect example). Probably the most important thing is not to show your project team a fake face, and to remain consistent (if you are tough with them, then remain tough, if you are soft, then remain soft, just don't be tough one day and soft the other day).
PS: I am assuming that being authoritarian is not mutually exclusive with being respectful and is not equivalent to being abusive (otherwise you have a big problem).