You're doing it wrong. If you're having that much trouble with deadlines and bandwidth, you should be inspiring your CEO, board, and investors to solve that problem. You should also make sure that you're providing them with honest estimates and not over-promising what your team can achieve.
Even if they do it willingly, pressing so hard on your team is going to lead to burnout and turnover in the long term, and lower quality deliverables in the medium term. Those almost certainly cost your startup more than a postponed feature or missed deadline.
As for inspiring the board and CEO etc. totally agree, but rarely is there a time an early startup CTO can tell investors we need to move slower. The best scenario generally is working to get more resources to reduce individual workloads but you still have to inspire people to work hard which will result in a number of long hours for some. And you can't be the "manager" just telling people to work harder, they have to be inspired by the work and what they are doing.
I also think it is critical to know how to transition your team to a more mature group as you raise further money and gain clients and revenue. Exactly to your point.
Any other time, it was a rarity, maybe like 3-4 days a year in case of emergencies. And this includes CTOs.
And understand that delivery is all that will matter in the end. Rough edges are expected, perfection is unattainable and shipping is most important. It is ok to demand a lot but pick everyone up along the way, dust them off and push them back into the game and get rid of bad hires quickly (you will have them). This will go a long way towards holding a team together.
You also should be highly competent and technical with ideally a reasonably broad background. People should respect your capabilities, not because you demand it but because you do the job. Remember you are never to good for anything that needs to be done, cause it all has to get done.