Why combine two problems working overtime without compensation and promotion focused culture?
As they say, the reward for being good at your job is more work. Expecting me to put in top effort for "the users" without compensating me doesn't work.
The idea that you can fix this with culture is wrong. It's been tried many times at many companies and it doesn't work for anyone but the owners. Unless you own a significant (let's say >5%) piece of the company, those late nights you work for "the user" will never be worth it to you.
You do not work for free. You are being paid. 'Top effort' needs not to translate to working overtime, more hours, etc.