Not sure what is meant by interesting point about the signing. This is what is from the SCYSA's minutes from Jun, "Any player transferring to another club, without their present coach’s signature on the transfer form, will be required to wait 30 days from the date the transfer form was received by the SCYSA State Registrar/designee before they can be rostered to another team. The player’s present coach may approve and sign the transfer form and the player will be released from their current team and eligible to be rostered to another team immediately upon the completion of the transfer form by the SCYSA State Registrar/designee."
"Should players/parents/coaches request transfers to a better team?" That's a question that can only be answered by individuals and their circumstances.
"If so, what circumstances should be considered? College scholarships, more playing time, attending better tournaments, or a need to win more games?" With the exception of the last one, these are all reasons I've heard about why people transfer. However, this is not the all inclusive list.