Do 3-way switches exist that don't "stick" in UP / DOWN position?
The problem is that you need some thing to "remember your state".  A simple mechanical switch shows it's state externally.  Now you are talking about something that toggles every time you push.  Probably possible to invent some rotary mechanism to do that... but there is this ROI issue.

There is a technology, used in commercial settings, not sure if it's cheap enough for residential, where a relay is installed on the light, and  on/off low voltage wires are run (in parallel)  to any number of  operational push buttons.  This allows n-way operation and even automation options.

http://www.kyleswitchplates.com/low-voltage-switches-plates/