Today is a time of both. There are circles where, baruch HaShem, the ranks of mechanchim‎{&&4}‎ are saturated. Even in those circles, there still is a purpose for one to go into a career in chinuch.‎{&&5}‎ It is possible that A is more talented and/or dedicated than B, who would get the position were A to go into a different field. Rashi seems to stress that it is appropriate to refrain from teaching only when the most qualified are already doing so. Furthermore, if A gets the position, it may force B to find a position outside of his natural community, where there may be a bigger need for mechanchim.
There are sectors of communities and, certainly, regions throughout the world (including Israel) where the need for all sorts of religious help is great. Much of the help can be provided by non-rabbis. However, we need many, many people, including “Torah professionals,” to go out and to reach out. It is mainly a question of whether you (if, indeed, this is a personal question) and those who know both you and “the field” feel that you have “what it takes” to contribute. “What it takes” is not monolithic; it depends on the specific nature of a given position, your God-given abilities, your level of idealism and perseverance, etc.
In general, if you have the desire to contribute, you probably are suitable. Chovat HaLevavot‎{&&6}‎ says that if one feels an inclination toward a certain profession, he should consider it a sign from HaShem. Presumably, this is all the more so in the area of teaching Torah, even if one falls short of the highest level of motivation described by the Rambam at the end of Hilchot Shemitta V’Yovel.