- This functionality already exists
- Making it useful would cause more harm than good
- It doesn't provide the information you think it does
The Mystical Profile
So you already have this in your profile (though you haven't filled it in):
In the year 2013, most businesses have a website. If employees of companies were to insert their webpage in to that field, you would be able to gather your data, huzzah!
But Nobody Fills That In!
Right, nobody does. So why would they if we added an additional company field? You can't force people to state their affiliation, and making them do it will not make users happy. I doubt your real name is rZaaaa.
The Data is Useless for Your Purpose
So let's say we do have a populated field for it. What does this say about the companies they work for? Unless they are only allowed to post during working hours on a work account about work, then a single person may be asking questions about a new technology for a pet project, rather than something appropriate to the type of work they're doing.
Companies that were doing sensitive work would want to hide the technologies their employees are working on lest someone get a reasonable idea of what the company is going to develop.
Companies that don't want their employees working on pet projects can search for employees of their company to see what they are asking about off-hours, and could use that against the employees in further interactions.
Just like looking at location stats, there is a lot of noise in the data anyway, and trying to do that with companies given the far more complicated issues involved is going to be even more of a hurdle if you want to do real analysis.
In short, don't hold your breath.