Link exchange requests still arrive weekly, and the useful skill is a quick assessment rather than a blanket policy in either direction.
Scale is what makes it a scheme
Two genuinely related sites linking to each other because it helps their readers is ordinary web behaviour and always has been. A systematic exchange programme with dozens of partners, tracked in a spreadsheet, is a link scheme. The difference is intent and volume, not the reciprocity itself.
The pattern is trivially detectable
Reciprocal links are visible in any link graph. A profile where most links are matched pairs with unrelated sites is a recognisable footprint, and it is the pattern rather than any individual link that carries risk.
The three-way variant is not a clever workaround
Site A links to B, B to C, C to A. This was a solved detection problem a long time ago, and anyone proposing it as a way around the issue is describing a tactic from a decade past.
The version that still works
Partnerships where the link is incidental to something real — co-authored research, a genuine integration, a shared event. The link follows the relationship rather than being its purpose, which is also why it survives.