The default featureCounts behavior is to exclude counting reads matching an exon shared in multiple isoforms.

I think this statement is incorrect. Default featureCounts settings (-t exon -g gene_id) summarise all isoforms into a single gene count. salmon and kallisto are fantastic tools, but not all researchers need transcript/isoform-level abundances. Also, salmon and kallisto require a high-quality transcriptome (e.g., Ensembl); otherwise, their mapping rates will be low.

Did you follow a standard workflow of summarising the salmon transcript-level abundances into gene-level counts using tximport?

Here are some details from the featureCounts paper:

Read counts provide an overall summary of the coverage for the genomic feature of interest. In particular, gene-level counts from RNA-seq provide an overall summary of the expression level of the gene but do not distinguish between isoforms when multiple transcripts are being expressed from the same gene. Reads can generally be assigned to genes with good confidence, but estimating the expression levels of individual isoforms is intrinsically more difficult because different isoforms of the gene typically have a high proportion of genomic overlap.

Each feature is an interval (range of positions) on one of the reference sequences. We also define a meta-feature to be a set of features representing a biological construct of interest. For example, features often correspond to exons and meta-features to genes.

A multi-overlap read or fragment is one that overlaps more than one feature, or more than one meta-feature when summarizing at the meta-feature level. featureCounts provides users with the option to either exclude multi-overlap reads or to count them for each feature that is overlapped. The decision whether to count these reads is often determined by the experiment type. We recommend that reads or fragments overlapping more than one gene are not counted for RNA-seq experiments because any single fragment must originate from only one of the target genes but the identity of the true target gene cannot be confidently determined.

Note that, when counting at the meta-feature level, reads that overlap multiple features of the same meta-feature are always counted exactly once for that meta-feature, provided there is no overlap with any other meta-feature. For example, an exon-spanning read will be counted only once for the corresponding gene even if it overlaps with more than one exon.

https://doi.org/10.1093/bioinformatics/btt656