You raise good points concerning implementation. They can all be addressed and resolved by not making an open-ended "fragrance-free" promise, which indeed has an element of subjectivity and could cause too great liability risks for hosts, but by creating a specifically defined "reduced fragrance" accommodation, with a clear list of do's and don'ts, and ruling out host liability for anything on The List that is not objectively verifiable.
I outlined in another post on this thread what such a list could look like. Checking the "reduced fragrance" box would oblige hosts to items on that list ONLY.
Guests would be notified that the "reduced fragrance" attribute comes with reduced host liability. The host is liable only if an item on the list is clearly violated.
For example, if a guest arrives and finds plug-in air fresheners, or toilet bowl fresheners, in the property, the guest can take a picture of these and prove that one of the conditions was violated.
Enforcement would mostly be through a new feedback system tailored to this accommodation. After every stay in a "reduced fragrance" property, guests would answer a number of yes-no questions related to The List, and assign an overall 1-10 subjective "fragrance free" score to the property.
With this, every host would build up a system of scores related to fragrance over time. Fragrance-sensitive travelers could relatively confidently book properties with high scores, and avoid those with low scores. Hosts could make changes in response to the score they received.
This system would be far more helpful for fragrance-sensitive travelers than keyword search, because it would actively educate hosts on what the community needs, and create a feedback system through which hosts can improve their fragrance-free offerings, and allow guests to avoid properties that are unlikely to work for them, without creating unworkable host liabilities.