In ancient times, Euripides was known as the philosopher of the stage and so, yes, I would certainly say that any of his plays are filled with "ideas."
Modern readers of Euripides' Medea need to keep in mind that this play was first staged in 431 BCE in front of an Athenian audience. At that time, Athens was on the brink of war with Sparta and its allies.
Thus, to my way of thinking, one of the most interesting moments in the play occurs when Aegeus, King of Athens, appears in Corinth and makes a deal with Medea to grant her asylum in Athens in exchange for her help in providing a remedy for his own childlessness.
Although many readers of the play have considered Aegeus' appearance in the play as strange and incongruous with the play's plot, the fact that an Athenian king enters into this agreement with a barbarian woman who will soon kill her own children strikes me as extremely thought provoking. On the brink of war with Sparta, Euripides' fellow Athenians were preparing to send many of their own children to die in battle.
What would Euripides' Athenian audience have thought about their mythical Athenian king making such a deal with this child-killer?
Euripides' audience may also have recalled that, according to tradition, Medea marries Aegeus when she comes to Athens and has a child (Medus) with him. Euripides' audience surely would have remembered that, according to their myths, before Aegeus had a child by Medea, he would have a child (Theseus) by Aethra, the daughter of Pittheus, whom Aegeus is on his way to visit in the Medea. Mythology also tells us that when Theseus grew up and returned to Athens, Medea tried to kill Theseus in order to preserve her own son's position as heir to the Athenian throne.
Thus, I ask again, what would Euripides' Athenian audience have thought about their mythical Athenian king making such a deal with this child-killer? Euripides has the Chorus of Corinthian women ask the same question:
How will this city of sacred streams,
this land of strolling lovers,
welcome you—a killer,
who slaughtered her own children,
an unholy woman—among its people? (Ian Johnston translation)