Not an expert, but...

As Wikipedia partly mentions, Shay designs were very well suited to low-speed operation on dirt-cheap (often temporary) tracks. That generally meant narrow-gauge, light rail & iffy roadbed, tight curves, and steep grades. Low-speed-only was the only sort of operation you'd want to attempt - tracks suitable for higher speeds would have cost far more, but provided minimal benefit for logging, mining, and other Shay use cases.

A bit fuzzier, but I also recall Shays being considerably more easily maintained (vs. conventional steam locomotives) in situations with minimal facilities, equipment, and trained staff. Not sure how much that was locomotives being designed to the customers' needs, vs. being intrinsic to the Shay mechanical layout.

And a bit of context - a century or so ago, modern heavy road construction equipment and heavy trucks mostly didn't exist. Vs. railroad tech did. So for logging, mining, and many situations where we'd say "d'oh, just build a road and use trucks" - they just laid some RR track and used that.