>>Wireless connections would certainly be more convenient, but I'd think they could be a pain to troubleshoot the more devices you have. And we're not talking about just *your* devices, but anything within range. Automagic operation is certainly convenient and desirable (from an enduser viewpoint) -- at least when it works as expected. It would be when it does something unexpected it could be a pain to troubleshoot. Physical cables are prone to clutter, but at least you can trace them and probably a tad less prone to interference.
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>Yes, but we do use that wireless approach for many other needs such as keyboard and mouse.
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>However, for now, I would be happy with a key to put on both ends. I looked at the other reference but that seems to be related to something specific about Google Chromecast feature. Would there be something available that we would just put key on the tablet HDMI port and another one on the monitor?

As for wireless devices based on transceiver plugs that effectively act like endpoints of a physical cable, ask a gamer why they don't like them. You're also likely to hear similar complaints from them regarding HDMI (as compared to "good-old-fashioned" analog connections for video and audio).