Athletically, lacrosse all year is fine (especially supplemented with the right strength and conditioning program)
Mentally, there are toughness attributes that a typical prep school, travel club kid does not have and will not gain on the lacrosse field. This is the differentiating factor for a multisport athlete. Football, Wrestling, Hockey and Basketball offer this (preferred sports in that order)
Football is 95% practice and only 5% games. Mostly pain, limited gain.
How many D1 Top 30 college football, wrestling, hockey and basketball coaches are telling high school recruits that they should be playing other sports?
I sugest that you go check the rosters of the top college programs in the sports that you mention. What percent of the players came out of private / prep high schools? What percent played for a "club" team?
Also, what percent of the top athletes competed only with their town team?