Was it like that for people who had been on the job for years, or just interns? If just interns, they probably had issues in the past with not doing it this way. You've got to earn trust etc.

Can't speak for Bloomberg, but its like that at any company that words on US Government contracts. USG accounting always requires time and materials records for every contract, even fixed price ones. That means everyone who works on USG contracts must keep a time card showing what contracts they worked on and how may hours they worked, completed daily. Every company expects their employees to bill an average of 8 hours per day for some period; at my former employer that meant 40 hours per week, while at my current employer it means X hours per calendar month (where X = 8 * workdays). Underbilling for salaried employees is covered out of company overhead.

Billing additional hours is a little complicated and varies based on the specific projects and company accounting practices. My current employer pays hour-for-hour for extra time billed, and we record all time worked. My previous employer had a hard cutoff at 40 hours (unless overtime was authorized), with the first 40 billable hours worked being what got recorded. If overtime was authorized for a given contract, one needed to work at least 48 hours per week on it to get paid extra, at which point you got paid hour-for-hour. I don't know why they did this, because the USG's preferred method for recording work hours by salaried employees who are not being paid extra is to record all hours worked but reduce the hourly rate accordingly.

Interns are managed differently because they're paid by the hour. Regular employees account for time spent on various projects, but that has nothing to do with your pay and is just a tool for accounting R&D time back to various business units for overall business planning.

I'm a freelancer and, from time to time, my billable hours come to a screeching halt when I can't get the client to tell me what they want done next.

It's a risk of the model. Part of why freelancers cost more per hour.