One can always retain individual FASTQs for archival purposes and combine them for analysis. Memory is a valid reason to align them separately, but I'd rather do one run with 48G RAM than 3 runs with 24G RAM given merging is on the cards anyway. Plus, BAMs are also intermediate files so I'd rather have a pre-processed starting point (trimmed + merged FQ) than manual intervention at the BAM stage.
But yes, most aligners accept multiple FQ pairs - most but not all. For example, the popular RSEM does not accept multiple pairs. You'd have to align using STAR then use RSEM from the BAM.
If the choice is between merging FASTQs or BAMs, I always go for merging FASTQs. Unless you expect the FASTQs to have batch effects (in which case you should treat the corresponding samples as separate samples all through the pipeline anyway), merging FASTQs is seldom a bad idea given you have sufficient compute resources for aligning the larger FASTQs.
Set aside issues such as memory footprint and file housekeeping, the operations are not commutative. For example, primary and secondery alignments may be mixed up when merging at the BAM level.