January 1952, Eisehnower announces that the US is damaged by the bitterness of partisan division. He proposes to seek the nomination of both parties
I don't think it's that weird. Is there anything in OTL that would have caused him to try this?
I can't see Ike being on both ballots in every state that had a POTUS primary, if indeed any.
This was before the modern primary system, most states did not have primaries.
Estes Kefauver won something like 12 of the 15 states that did have primaries and Taft had a small lead over Ike in the Republican ones. So any ballot issues would not prevent this.
Magniac, Bryan ran under the endorsement of the populist and Democratic parties. I'm not sure how delegates were involved, however.