The reasons athletes choose to pursue the path of a walk-on are numerous. Here are several more common reasons:
The athlete is already receiving praise, but the school they are particularly interested in does not share the level of interest. This target team could either be considered more athletically prestigious, it may already be saturated at that position or the athlete chooses that school for purely academic reasons over others. The walk-on will join the team to try to win the coaches over.
The athlete may be a scion of a notable former player, alumnus or coach of the school. Often these players do not strive to be placed in a starting position, rather carry on the tradition of being a part of a particular team.
In the case of punters and kickers, there may not be a scholarship available, but the coaches may have encouraged or invited them to join the team without offering an athletic scholarship.
An athlete may have just been homeschooled during high school and was unable to play on a team, and therefore, not receive any attention from scouts.
Athletes also walk-on after playing at small high schools, which also limits the attention paid by college scouts.
In some instances, a college coach/recruiter may designate an athlete as a "preferred walk-on" during the scouting process. In this situation, the athlete is assured a spot on the team, but the coach is unable or unwilling to offer a scholarship.
Many schools that do not provide athletic scholarships actively recruit student athletes, and these students can get admitted to a school with academic records that are below average for that school. The Ivy League, for example, does not permit athletic scholarships, but each school has a limited number of athletes it can recruit for each sport.