It isn't about working from home. It is timing. Are you going to ask someone to marry you on the first date? You are on a contract, not an FTE. There are dozens of other qualified people who desperately want jobs, who would happily come into the office.
The right way to approach this is to show them how fantastic you are, why you are so good, and then when you bring it up, they will feel like they have to consider it because they don't want to lose someone so good.
I think you are right in that some companies have an outdated way of thinking, but I also think the inverse is true, that employees are blind to the fact that people who are co-located in an office space tend to be more productive. What does that mean? If you have an office of 50+ people and that is your central base of operations for a small organization, you will accomplish more working in an office. If you are a large company and you have an accounting and finance hub of 150 in Chicago, those 150 people will be more productive working in an office than if they were all remote.
If you are a global organization with small cohorts around the world and there is no geographical consolidation to your department structure, then yes, wasting time commuting to an office for the sake of having an ass in a seat, is less productive.
Employees refuse to consider the former, employers refuse to consider the latter.
Also, no offense, no good manager should trust someone brand new. Trust is built and earned, not given. I wouldn't allow someone to WFH for at least 6 months until I understood their working habits, strengths, weaknesses, productivity, etc.