I'm not convinced of this supposed horseman solution. Firstly there is the opportunity cost of not researching CoL/Sanitation/Religious tech. Secondly, I think a Str4 unit attacking a Str 5 unit with probable defense bonuses will be feeding XP or simply giving the Sheaim player an easy decision over which PZ to suicide against cities. If the horseman wins then I wouldn't give good odds on his survival. If the PZs are in unroaded forests/hills (probable in the early game) then the Horsemen may not even be able to withdraw properly.
Finally, what use are these giant horseman stacks except on defense?
Does Brigit have any fire immunities (Angel of fire etc)? Also, high unit level has been confirmed as reducing damage received in this situation.
1. NEVER have any forests in the first city ring of a border city.
2. A horseman with one upgrade has 45% withdrawal chance and so you lose only about every second new built rider, but also about every second rider manages to reach what you wanted - to damage your opponent. If you manage to withdraw you get another upgrade --> 65% withdrawal chance. These units certainly won't die as you can move them to another tile save from exploding PZs. With all PZs being damaged it shouldn't be a problem to kill those with other horsemen promoted with strength and shock (Or other units. See point 7).
3. Not getting killed is quite a fair trade for researching a tech that's not that expensive, so not being able to research a builder tech is not an argument for me. With that argument you could as well say: Why should I research bronze working? Iron working? Any tech that offers you a military advantage. Additionally horseback riding is on the same path as trade which boosts your research AND you can give your units mobility1 what's a good thing for builders (For example you can give disciples mobility1 to spread your religion more effectively) and for warmongers.
4. Horsemen can be built in every single city and can be brought near the attacked city very fast, so having that giant stacks of horsemen is not that hard. Your opponent moves only with one point of movement while your units move at least with 6 points of movement (including roads). His units need longer to get supplies. Often the AI attacks through the borders of another AI and thus ignore the logistic problem they will get in that war. With riders your logistic is always good.
5. Horsemen ARE a good offensive weapon because of their withdrawal chances, their mobility, their boni against archers, their ability to pillage important strategic resources without bigger efforts... I have won some games nearly exclusively using horsemen (in the late game I used horseriders but that was it)
6. If the Sheaim are adjectant to you from the beginning and you don't want the challenge of a PZ attack you have enough time to kill him with warriors. A warrior rush can be done by everyone and is not that hard to do.
7. There is another good strategy against PZs I often use. If they are still two tiles from the city you can move the other units you consider to able to kill the PZs on a tile next to the city with a road. The turn after you move them indivually into the city and attack the PZs. This way you can assure your other good attackers don't get any damage by exploding PZs as they are safe on another tile. Additionally if you give the attacker mobility1 you can even move him back to the tile from where he came from to assure the explosion damage of later units doesn't kill him. This strategy can be combined very effectively with the huge horsemen stacks as it'll be easier to find apted attackers as after the attack of the withdrawal horsemen PZs are weakened.
Concerning Brigit:
I found that save game and I had promoted Brigit with magic resistance (20%) and fire resistance (50%). With the knowledge that the Angel promotion gives 20% fire resistance it's clear why she wasn't damaged a lot.