Solder between IHS and die means that there is a through and through metal connection. This results in a low thermal resistance, allowing better boosts and overclocking and/or lower temperatures. (This is the best we can currently do with flip chips; in power electronics direct bonding to a metal substrate is used instead, which results in even lower thermal resistances, and thus higher power densities).

However. Soldering these is quite difficult with smaller dice and thermal cycling can result in cracks which impacts reliability, because silicon, the solder and the IHS have different thermal expansion coefficients. There are multiple processing steps required and the solder used is of course special as well. (In fact, in the article you can see the gold plated areas on the nickel-plated IHS where the dice make contact).

TIM (i.e. thermal paste) is very easy to apply and has a predictable lifespan pretty much regardless of die size. The thermal resistance is much worse, though.

Solder must be heated to a high temperature in order for it to flow, which it must in order to properly bond the die to the heatsink. CPU dies, especially those using modern sub-50nm processes, are extremely fragile. Using an assembly process that requires the die to be exposed to high temperatures (up to ~200C for the types of solder used by chip makers) will increase the total assembly time and decrease yields in terms of good chips making it out the door.

The soldering process requires precise thermal control and cycle control. Get the solder just a little too hot or put a little too much on the die and you'll overheat it. Heat or cool it down too fast or far and it'll crack. Compare that with what is needed to squirt a pea of thermal paste on the die and slap the lid on and you'll get why it makes sense. Die yields are already low enough with the latest ultra-tiny 14nm-and-below processes, losing a good die to the "easy" part of CPU manufacturing (assembly) is very costly.

What I have read is that with small dies solder will eventually start to fail. On larger dies it's less of an issue.