So four free temples is awesome, granted. BUT, as pointed out here, you have to delay a while and really work to make the stars align to get them in reasonable time. This is particularly problematic when you want to rush through Tradition to get its very strong finisher. Last game I took Aristocracy and Oligarchy first and then the piety opener while I waited to get Philosophy and some monuments up (caveat: Philosophy was delayed by the Hanging Gardens). And I really wonder whether it was worth all the mucking around (and I still only got three temples - if you're taking Tradition, you're unlikely to be expanding to four cities that quickly).
I'm tempted to think you're going to get far more overall advantage by taking Legalism straight away and getting those monuments early. It's very quick to get to the second Tradition policy now, so you could easily delay the monument in the capital and build something else instead. And by not having to build a monument in new cities you get them up and running significantly quicker, and that's going to give you some really big turn advantage (you could buy them, granted, but now you get the monument and can buy e.g. a granary instead). Is a temple as good as accelerating a new city's development by that much? I don't think so, personally.
The other advantage is that you're generating more culture earlier, getting more policies more quickly - particularly Monarchy (or the piety opener so you can build those temples more quickly)
With the finishers, I don't think dabbling in multiple trees at once is the smart move it once was. If you're planning on going Tradition + Liberty, I can definitely see going for Tradition opening then Liberty then Legalism, but if you're focusing on Tradition, I reckon going straight for Legalism might be the smart move.