The cover makes the bike look like a piece of luggage. It allowed me e.g. to get the bike on-board as a carry-on on an airline which would knowingly not allow for that and which would normally take bikes only with a bike fee. At times, for one reason or another, I do not test the policy of my lodging towards bikes and if I put a cover it is nobody's business.
I agree 100%. The Brompton cover is relatively inexpensive (all things considered), takes up very little room, and really helps "hide" the bike so that it doesn't draw attention to itself. It helped me out considerably on the train once because of their nonsensical baggage/bike policy (Amtrak). On the return trip, I threw the bag over it, opened the top just a bit to grab the saddle horn, walked on, and tossed it into the overhead rack. Nobody cared.