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This is not obvious at all.

Neither does it ever mention current mode.

Your case seems to be based not on any information from power integrations, but rather your own intuition as an engineer. Understandable, often we have to fill in the gaps with our best judgement.

My own intuition doesn't see any issue with voltage-mode control so long as one is willing to accept a very low crossover frequency (I consider ~1KHz to be super low). Ultimately crossover frequency is going to be restricted by the RHPZ regardless of whether CMC is used or not. Voltage mode imposes a little extra penalty, but likely not an issue if you're already willing to accept such a low fc.

But consider AN-57 (which the OP also mentioned), which explicitly states several times that TOPSwitch parts are voltage mode, including transfer function plots showing the classic second order response. Nowhere does it mention current mode control or anything similar to it. It's unclear if this document actually applies to all TOPSwitch families; the only specific families I can see referenced are GX and JX. The JX series, at least, also has contradictory plots showing peak drain current and duty cycle being directly dependent on control current.