The whole point of sycophancy is that it’s invisible to the person on the receiving end … you don’t request a skeptical mode when you don’t realize you need one.
Certain kinds of skepticism could be the default. Before endorsing a policy or factual claim, the system could ask what evidence supports it. It could also give a serious counterargument and state its confidence.
That would slow the exchange down. In some research or policy contexts, the delay may be worth it (Interface friction).
Valid claims can get over-questioned, which creates false negatives, and users may perceive neutral skepticism as hostility. There is also latency and cost overhead from the extra reasoning steps.