Zevachim 17: Does a Mitzvah Done While Ritually Impure Count as a Mitzvah?

Some thoughts from today's daf:

• A person who is tamei, in a state of ritual impurity, cannot participate in a number of rituals
• If a person who is ritually impure does participate in Temple rituals, their service is invalidated 
• A similar question: must a man go to the mikvah, the ritual bath, every morning before reciting his prayers?  
• What if a man had a seminal emission during the night?  
• Will his prayers be nullified if he does not pour at least 9 day of water on himself? 
• The Jerusalem Talmud says that it is permitted to bathe and to engage in marital relations
• how could it be that someone who is ritually impure would bring a sacrifice/engage in prayers?  
• The rabbis argue that the Jerusalem rabbis were lenient
• More people should have been strict about going to the mikvah before prayers/service in the Temple
• Before every prayer people should go to the mikvah

The notion that prayer is a direct substitution for Temple rituals is challenging.  Bringing a sacrificial offering is so visceral, such a limited action within time and space. It is externally focused and measurable. Prayer, on the other hand, is long-lasting, internally focused, and extremely difficult to measure.  How can we expect people to adhere to the halachot of prayers when we had difficulty with the 'simpler' rites of offerings in the Temple?