I would even venture to say you don't need all tall forwards depending on formation and skill levels - better to mix it up, give the defense different looks and styles of play to deal with, and exploit the mismatches.
Completely agree. Tall forwards are good for over the top and chase it kind of tactics but not a discriminator for possession-based attacks. I know everyone points to Messi (5'6"-ish) but look at many other successful forwards (e.g., Aguero, Naymar, Griezmann,...) and none of them are more than 5-10ish. Ibra is an exception, along with Christiano - both over 6' tall. Luis Suarez, who I consider to be the most complete forward player today, is 5'-11".
As for winning headers, there are two components in the equation. Timing and vertical leap ability. Many shorter players win headers over taller. What you care is the players ability to jump high (for the ultimate vertical reach) and ability to read the ball for timing the jump. The key is to execute the jump at the right moment.