Don't see why. Not many phone chips make enough heat to make the pipes feasible. I can see the advantage but I mean what's the gain? No chips get hot enough to cause significant leakage. Heat pipes would allow more powerful chips, but then you'll kill the battery before lunch. A lot more R&D needs to go into the battery tech first, not cooling and screen resolution.
Now that I have a data plan worth using, my phone batter last me 9 hours. That's enough sometimes but other times it's a major pain. Give me a 3000mah battery before beefing up my already plenty fast phone. Thanks.
Maybe better cooling will allow for a better battery in the future, but I agree adding cooling will only allow for a more powerful phone, meaning higher power draw, because that's really all the heat is, power. Although, I have a Nexus 5, and it gets hot and has huge throttling issues, so a better cooling system would help. I think that better cooling will help a lot of phones, but if it exceeds the phone's heat output, they'll just increase the power usage, making the battery life even shorter. You can't upgrade the cooling without upgrading the battery, basically.
Sure, this would improve the throttling issues current phones have - I've seen Snapdragon 800 doing worse than S600 that in turn was doing worse than S400 in overall performance due to throttling (kids messing with the phones - playing games, etc.).
The end result would be more powerful SoCs and the same throttling issues as before and even more pathetic battery life.
Also, the heatpipes would just spread all the heat generated by the SoC to a larger area, therefore making the whole phone hot - not to mention more expensive. For a PC, that is fine, but for a phone that you hold in your hands, that's undesirable (at least for me).
The heatpipe would be useful if the SOC could clock up when plugged in. Then the phone could do a lot more BOINC (distributed computing) work when plugged in or use more sophisticated software without bogging down. But I think it's use is limited because without heatpipes they can still design a phone where the chassis is the heatsink. With a heatpipe the only real advantage would happen if there was active air flow I think.