Managing based on time is like pushing on rope. Assuming there's no actual slack, you can either spend more money or cut quality, and in the short term more money may not be faster (see Brooks' Law). You have to manage quality and cost directly with time as an output.

Making an explicit decision to go with first-draft quality has a name: it's "accruing technical debt" and sometimes it's justified, as long as you're aware that the long-term costs go up when you make a short-term compromise on quality.

Trying to manage on time directly also has a name: "death march". It also has severe long-term costs, both in quality and staff turnover.