Eddy's correct that a big put off with router machines is the speed or more impotantly acceleration and speed together is a lot higher for 3D and laser.
This causes a conflict of interests in the way the machine is built and components esed.
For instance good engraving requires high resolution and stiff machine so smaller pitch screws are needed but this slows the machine down so acceleration and speeds required for 3D/laser is not reachable with steppers.
Routers are some where in between but then they need a much stronger design which starts to slow things down regards acceleration, so again very difficult to reach acceleration and speed required for good 3D/laser.
Then you have all the difficulties of each having there own business ends which don't mix very well.! Saw dust, high heat and molten plastic don't really mix very well. Changing out each one isn't as easy as it sounds so thats not feasible in reality and will soon become pain in the arse.

Regards 3D printing then the technology is so cheap and easily available it's not worth struggling to make a combi machine that will be compromised when you can have the real thing.
Also while mach3 can fullfill all three requirements all the action and software 3D printing developments are happening on the Arduino based systems so it will always be behind in technology. Programming isn't required for 3D so thats not something to worry about.!

Poppy Ann I've built a machine that lives in Mansfield and I will be calling there some time soon to give it a check over. So if your available then I'll gladly call on you for a Cuppa tea and chat.