It is easy to conclude that your cavalry and infantry are more precious as compared to an icon or an artifact that is stored in your monastery in your Age of Empires game. This is particularly true when you have a military oriented objective like destruction of the town center or capture of the castle.
However, you should not forget that storing a relic or an artifact in your monastery will help you earn lots of gold without any difficulty. Once the relic is in the monastery, the quantity of gold in your stockpile will be constantly rising.
The rate of increase may not be very high but it will make a huge difference to your resources in the long run. Once you focus on defensive positions and return back to your offensive strategy, you will be surprised to discover that your stock pile of gold has increased by a significant percentage.
Hence, there is nothing wrong in having a few scouts scour the territory specifically for the task of finding relics. Of course, the entire strategy is based on the presumption that there are relics in and around your map. If you know that there are no relics, then do not waste your time and focus on your military objective.
Another advantage of having relics is that it is going to improve the status and prestige of your monastery. You can make use of the gold to improve the power of your priests to resist conversion and reconvert other enemy troops and buildings very quickly.
Converting the castle of your enemy is the simplest and most effective way to win the game. If you have an army of monks to take over this task, you will discover that the entire game can be won without any emphasis on the military angle. Needless to say, you will need numerous relics as creating lots of monks is going to cost you a lot of gold.