2) JH and other dissenters, why do coaches have players tuck their shirts in? It certainly doesn't affect performance.
There is no such rule in Major League Baseball. Players don't have to tuck their shirts in.
From MLB:
1.11
(a) (1) All players on a team shall wear uniforms identical in color, trim and style, and all players uniforms shall include minimal sixinch numbers on their backs. (2) Any part of an undershirt exposed to view shall be of a uniform solid color for all players on a team. Any player other than the pitcher may have numbers, letters, insignia attached to the sleeve of the undershirt. (3) No player whose uniform does not conform to that of his teammates shall be permitted to participate in a game.
(b) A league may provide that (1) each team shall wear a distinctive uniform at all times, or (2) that each team shall have two sets of uniforms, white for home games and a different color for road games.
(c) (1) Sleeve lengths may vary for individual players, but the sleeves of each individual player shall be approximately the same length. (2) No player shall wear ragged, frayed or slit sleeves.
(d) No player shall attach to his uniform tape or other material of a different color from his uniform.
(e) No part of the uniform shall include a pattern that imitates or suggests the shape of a baseball.
(f) Glass buttons and polished metal shall not be used on a uniform.
(g) No player shall attach anything to the heel or toe of his shoe other than the ordinary shoe plate or toe plate. Shoes with pointed spikes similar to golf or track shoes shall not be worn.
(h) No part of the uniform shall include patches or designs relating to commercial advertisements.
(i) A league may provide that the uniforms of its member teams include the names of its players on their backs. Any name other than the last name of the player must be approved by the League President. If adopted, all uniforms for a team must have the names of its players.