I agree that “gapped” offers are not desirable. However, I don’t think it’s necessary or even wise to limit your list entirely to full-need-met schools. There are many good colleges that meet a high percentage of student need and also give merit to strong applicants. When the applicant is well qualified, it is not at all unusual for merit to fill any gap left by the need based aid, and also potentially to replace loans that are part of the need-based aid package. You can miss out on some great opportunities by ruling out such schools out of hand. Look instead at the average percentage need met - if it’s close to 90% or above, and the applicant has good merit potential, the school deserves consideration.
Edited to add: It’s also the case that some schools stretch to declare themselves full-need-met for exactly this reason - it’s attractive to applicants. However, since it’s a stretch for them, they may use the least generous formula possible in computing your need. In this case, you can actually end up worse off. Even if you’re granted merit, it will not “stack” but will be absorbed into the overall aid package, leaving you at the relatively high net price the school computed. Net Price Calculators aren’t a guarantee but are definitely your friend in terms of gauging what a school will expect you to pay. Ultimately this is more important than the distinction between a full-need-met school and a “meets 95% of need on average but also gives merit” school.