yeah I made the same point. It is 37 hammers for each point of faith vs. 40 for each shrine and no maintenance. On low levels the investment makes sense for this reason, I will admit I was only thinking for immortal and deity which is what I play with AI. there is a chance you get it at these levels, esp. on standard and small worlds if you get lucky to have few AI with religious flavors but on large and huge maps which I often play there is virtually no chance. Someone like Celts, Ethiopia, Egypt, etc. is there and they always build it way earlier then I get the chance. Plus beelining calendar is a poor choice anyway. There are more important techs like animal husbandry, writing, and mining.
However, the hammer savings of 3 hammers neglects a few things that would make me still opt for shrines in some games:
1. You build shrines in 5 different cities meaning you can get a shrine in your first 2 far faster then stonehenge. Esp. in capital.
2. If you opened liberty the extra hammer applies in each city as does the 5% bonus to buildings from republic making shrines the cheaper option. Also you are pumping out settlers so no time for stonehenge not to mention risk of losing.
3. Early faith is arguable far stronger then late faith bc of the way pantheon costs scale. The delay on stonehenge will mean a lot of lost pantheon choices and extra faith spent on the pantheon since the cost goes up with each prior pantheon.
4. If you go piety opener shrines AND temples are by far the cheaper hammer investment compared to stonehenge but you do have to pay maintenance.
In summary, even on the lower levels I'd still build shrines preferentially with both the liberty and piety strategies. You get the opportunity a lot earlier and all those turns of an extra 1-2 faith matter a lot because of the way the pantheon race works. Alternatively, for a tradition opener stonehenge is attractive since you've focused on growing you city and get a 15% cost reduction on wonders and don't have to produce as many early settlers to be competitive. If you have solid production and some forest to chop it could be done with no threat from AI pretty quickly emperor and below. I could see it being very valuable in this situation. And you could always still build shrines for even faster religion.