Ortiz and Jeter were the last two truly big names I remember seeing getting spots in non-baseball stuff. Small wonder that they were two of the biggest stars in the game and both played for "storied" franchises in major media markets.
Also, let's be honest here: there's a major reason baseball stars are not national stars on the same level as the NFL and NBA. It's four letters, all capitals, and based out of Bristol, CT.
ESPN pays lip service to baseball in season (and during big stories), a little more than it does to hockey, but football and basketball DOMINATE those broadcasts like nothing else and the stars of those sports are promoted most prominently by the programming. And if you don't want to just chalk it up to ESPN, there's also the fantasy component: football (especially) and basketball are the two biggest fantasy sports, as far as I know, and get the most attention for individual performances as a result (consider that offensive football players get far more attention than defensive, which corresponds to how fantasy football typically deals with the non-offensive side(s) of the ball).
Beyond that, football and basketball have bigger footholds in certain demographics, especially non-white, and probably have more eyes on them on a daily basis than baseball does.
MLB should be promoting the shit out of Trout, Betts, Bregman, Bellinger, Rendon, etc., and trying to make them household names the way some stars of yesteryear were but are just behind the 8-ball because the biggest promotional network is only barely on board with the sport and the fantasy machine is solidly behind football and basketball more so than it is baseball. MLB needs to find a way to fix that if it wants baseball to climb back to the top. So long as its a third-class citizen sport to ESPN and fantasy, it'll be so when it comes to stars.
The NHL has it even worse.