There are plenty of reasons why he didn't go that way, mainly related to overall geopolitical strategy and his good luck in being able to muddle through, have his cake and eat it too by thwarting the electoral provisions of Geneva but also not needing to send troops.
..but what if Ike writes off South Vietnam as hopeless, and leaves France holding the bag through the proposed election, the commies win and he tsks tsks thhe whole time.
What is the domestic political impact in 1956?
Besides having Republican boosters, Diem and the anticommunist Vietnamese cause had several Democratic boosters at this time (mid-50s) including Senator Kennedy but also people who later became war skeptics like Mike Mansfield and Hubert Humphrey.
If they see him as too passive, how effective would the Democrats be at using this against Ike? How vigorously would the Democrats even push this?
Would they make any popular vote or electoral vote gains for Stevenson, or gains in Congress, in 1956 as a result?
On the one hand its tempting to get revenge for "who lost China" charges, but then again, who really wants another Korea in the mid-50s? And wouldn't such complaints be transparently political and rhetorical, and thus less resonant with the public?