How and why are byes given in tournaments when there are plenty of players to be matched up? I do not see the point in joining a tournament simply to sit out rounds.

Simple. If there are an odd number of players in a section, you will end up with a bye each round. In USCF tourneys, it is usually the lowest rated player with the lowest score that hasn't already had a bye.

If there are multiple sections, sometimes pairings can be made across sections, if both have an odd number of players. It is also possible that some players may request byes in some rounds making the available number of players odd, causing another bye to be given.