I think about a prayer as a form of Hachnasas Orchim, welcoming guests.
Hillel said “is not the soul a guest in the body? One day it is here and the next day it is gone.” 
Shlomo Hamelech teaches that one who develops and does good for his soul is considered a person that embodies Chesed.
What if we looked at prayer as our once in a lifetime opportunity to accompany our soul on a walk with Hashem, a time to support our soul to attach to Hashem, a time to support other souls to also attach to Hashem?
We can develop this when we take the three steps back we take and then forward to begin our Amida prayer as an opportunity to practice the mitzvah of Hachnasas Orchim.
When we take our three steps back, we can invite our guest, our soul to join us on our walk with Hashem, the path we choose.
We can take a survey of our soul and make sure we know what our soul needs to request or express. We can make sure our soul is properly prepared to meet Hashem; in the same way Avraham Avinu made sure to wash the feet of his guests before bringing them in his home.
Did we make sure we understand the needs of our guest (our soul) and any other guests (other souls) such as our friends, our nation we daven for. Is it blessings of food, and drink that is needed? What type is appropriate? When is it needed? How much is needed? Do we have a need-to-know Hashem in a new way? How do we want to ask for that? Do we need healing; what type of healing is needed? Is it Teshuvah, is it compassion, what blessings are required for our soul? How can we best take care of our guests? Have we taken the time to sufficiently recognize the good of our soul? Are we careful in how we speak to our soul? Have we made our lofty soul sufficiently welcome?
It seems to me that the more we treat our souls kindly; by using thought and kindness to our soul, Hashem responds with even more! Once we have prepared for our guests, we can then take our three steps forward to talk directly to our Creator in a whole new way.
Perhaps this is why we learn from Avraham Avinu that he asked Hashem to wait for him to greet and take care of his guests rather than receiving the visit of The Divine Presence. Perhaps he was davening, preparing himself in this way in order to properly have a visit with The Divine Presence.
The reward one receives for accompanying guests is even greater than these mitzvos of chesed that is considered to be immeasurable such as visiting the sick, comforting mourners, preparing for funerals, attending to the needs of a burial, mourning, digging a grave for the deceased, bringing joy to a bride amongst others.
Avraham Avinu instituted the path of Chesed which he would feed and provide drink to people who were passing by in their travels and accompany them. Showing hospitality surpassed receiving The Divine Presence. Chazal teaches, whoever does not accompany them [guests] is considered as if he shed blood.