Hi Chris,
You are correct that keyword stuffing is no longer a legit SEO practice, and it is not ideal for user readability. Can you still get away with it sure. However, it is not a long term strategy as at any moment Google can pull its plug on you and de rank or penalize these efforts.
A better approach is to rank one keyword per page, you can rank for all the terms and potentially even higher then trying to rank one page for 3 terms. This is a better approach for users and Google alike.
To step into the shoes of the competitors. There was a time when the competition was low and ranking for multiple keywords per page was doable and so you had limited pages, and many words to rank for, so that is what you went after. Back in the day keyword stuffing was the way to go. As a result, companies such as Morton Buildings could easily rank for them. Currently they have built up the authority and the traffic for these terms, and so they are easily ranking top position for short tail (two word) competitive keywords. So in their eyes, they may even have in-house SEOs that understand that keyword stuffing is a no-no; however, they are currently ranking for these terms, and they may not want to touch and change what is not broken in their eyes. As soon as Google or other search engines take action on this, they will have to take appropriate measures to change and fix things up.
Again, for someone starting out in small business, at this point, going for multiple keywords per page is not a realistic approach. You have much better shot going after one keyword per page. Even a long tail keyword such as "small wooden horse barns" vs competitive "horse barns" to try to rank competitively.
Hope this helps!