I don’t think there’s anything bad about quoting an hourly rate. Shows where the money is going and sets up the turnaround expectation of how long it will take. Also makes it clear how much it will cost on extra changes and how much you are worth in experience to other professionals they pay hourly like their lawyer, accountant, etc. Ultimately most of those other costs (materials, production, etc.) boil down to hourly rates for extraction, assembly, anyhow.
I use a combined approach usually for larger projects. Outline the budget by phase with hourly estimates and rates, but invoice as a fixed cost. This way I don’t have to track hours (I’ve worked enough to know how long it takes), the client can see where the money goes (I didn’t just pull a number out of my head, and harder for them to lowball, as I can go back to the budget and ask what hours they’d like to reduce). If they take your word about how long things take as you are the pro, there’s very little negotiation tactic on their end. Also allows me to give a bulk discount for a new client or special project on the bottom line while preserving my rate for future work. Upping the rate also easy and clear as s year to year cost of inflation.
End of the day, there are many strategies. What works for you may not work for others and it depends on your type of clients, projects, industry, etc. one thing for sure is that as mentioned better to push your rates and see your limit even if losing some work, then under charge.
Also, pick work and clients you like and the rate doesn’t matter as much mid rather make less on work I love then more on work I hate. Best to make more on work you love, of course 
R