Let me start by stating that I will not touch on the economics of the issue, but I am a History professor and my chosen field of study (and passion) is Medieval and Ancient Warfare. Now, about the issue of permanent bridges and forward bases:
I caught myself thinking why they did not used those, every single time I was reading a battle scene. Permanent bridges, be it made of metal or stone, are just ideal for the type of war they are fighting here and they don't need to worry about 90% of the problems of building and maintaining such structures because of soulcasting.
The "problem" of the Parshendi using the bridges is actually inexistent. They already can run through the Shattered Plains on foot, jump over the chasms and arrive for battle without adverse effects. Bridge or no bridge, they way be battle-ready, so the creation of permanent bridges only helps the Alethi without helping the Parshendi. Again, no reason not to build them.
They also don't need to worry about the Parshendi destroying the bridges. If it is made of stone, reinforced with pillars and everything, then I wish good luck to any man trying to destroy them with hand-held weapons. And the Parshendi don't use siege weapons so... They will be pretty safe, I think.
Now, about the fortifications. I believe that building a structure on top of the stone pillars will make them too vulnerable to the storms. The solution is actually to build them inside of the stone! With soulcasting, they could hollow a pillar in no time and turn it into a perfectly protected and resilient fortification. And if they are cough in a siege (what I believe is impossible in the Shattered Plains due the storms), they just can use soulcasters to generate food and water until help come.
Now, about the other issues people raised:
There goes the argument about religious implications. They use soulcasting to get rid of human excrement. There is not much less holy than that.
And there goes the argument about costs. And if this don't convince you, they could just use good old engineering. I believe this would be MORE costly, actually.