EA: "There isn't much room for other titles than 1st party on Switch"

[Leynos]

EA has never played in the success or failure of a Nintendo system. Just as an example. EA support was gone on Wii U after launch. They also supported Gamecube pretty decently. They also only put 1 or 2 madden games on DS, other than that EA only put out shovelware. No one has ever said Boogie and My Sims Racing was a factor in DS sales.
EA supported PS Vita better than 3DS.

That said EA is missing an opportunity to have portable Dead Space, Mirrors Edge, Mass Effect. I do think those would sell.