“I actually think that the spike narrative is overblown”
I don’t think it is overblown so much as mis-defined. High schoolers seem to have the idea that a spike is the golden ticket, and, being overly optimistic in general, think they can create a spike fairly quickly (one summer, according to one recent hopeful CC poster).
In reality, it often takes much longer to gain the level of mastery needed to stand out at a top-in-the-field level. According to Malcolm Gladwell, “10,000 hours is the magic number of greatness”. Try fitting anything remotely close to that into your four years of high school! Even if the student hasn’t quite reached 10,000 hours, a perceived spike will be attractive to tippy top schools because the student will have achievements and awards at an unusually high level for a person of his/her age. It’s an easy bet that the student has potential to do even greater things, hopefully something that will bring favorable publicity to the university.
A high schooler aiming for a spike is far more likely to just be merely “pointy”. Pointy can be okay if you’re going for a particularly unusual or rather difficult major - as long as the student has not completely neglected the cores. Otherwise it is not any better than being well-rounded.
To the OP’s question, though, yes, a student who is genuinely nice and loves learning will find a place. Top colleges love those qualities in students too! A “Renaissance Man” can have multiple majors. But choices still must be narrowed and made, but not necessarily in high school. Most colleges are happy to give students a year or two to explore. The entire expression, however, goes “Jack of all trades, master at none.” At the end of the college years, the job market places more value on the master.