Euripides had a tradition of not just supporting the cause of women, but also of slaves, and it is interesting that in some ways the Nurse in this play is presented as being the most sensible and wisest of all characters. It is she who observes what is going on around her and what is happening to her mistress, Medea, and concludes that it is much better for people to live a normal life than try to live a life that is special or extraordinary. Note what she says after witnessing the life of royalty:

Ruthless is the temper of royalty:
How much better to live among equals.
Let me decline in a safe old age.

To the Nurse, from what she has observed, she recognises that to live a life of privilege is only to face a life that is above all else "Ruthless," as is shown through the way that Medea is treated by Jason. Her words therefore are incredibly wise. It is much safer to "live among equals" than to try and live a life that is defined by great status, prestige or wealth. Her prayer is to be allowed to "decline in safe old age," which shows she values a simple but uneventful life over one that others might feel they desire. This is a very sage example to follow in today's world, where we crave celebrity culture and all wish that we might be catapulted into stardom. It is clear the Nurse would have some very strong words indeed to say about such a desire. 

In Medea, why does the Nurse prefer not to be great?

In many respects, the significance of the Nurse suggesting that she does not prefer to be great speaks to the humility that Euripides suggests is needed in being a human being.  In the opening of the drama, the Nurse clearly establishes that Medea's intense nature, one that demands a sense of satisfaction out of hubris and individual ego, is a destructive force.  When the Nurse describes how Medea is looking at her children as "a bull," it is a reflection that Medea's own ego and sense of self has taken over her identity. Invariable, the Nurse believes that this will lead to a saddening end.

The Nurse praises the value of moderation and not of achieving individual greatness.  Medea is one who sought the prize of individual greatness in her willingness to help and love Jason.  The result of that pursuit is the sadness that sets the tragedy in motion.  In rejecting greatness, the Nurse's statement about moderation in the opening of the drama speaks to the path that a human being must pursue in order to find a pittance of happiness in this life:

....at any rate, I hope
to grow old securely in modest circumstances.
First of all, the very idea of moderation  
wins first prize in speaking, and in action,
is by far the best way for mortals, but excessive power
can produce no proper return for human beings,
instead giving back greater madness
whenever God is angry at the house.

In this explanation, it becomes clear why the Nurse prefers to defer greatness for moderation.  The Nurse clearly indicts Medea for coveting "excessive power" and a sense of individual greatness and thus invoking the anger of the Gods upon the house.  At the same time, the Nurse's desire for moderation and deferral of greatness is what she believes represents "the best way for mortals."