The quote comparison search is not winnable and not worth chasing
Those terms belong to companies whose entire model is built on capturing them, and an agency cannot outspend either category.
Direct writers advertise nationally at a scale no agency approaches. Aggregators and comparison sites exist specifically to rank for these searches and monetize the contact afterward.
The searcher is also usually the least valuable kind. Somebody comparing quotes on price alone is shopping a commodity, will do the same at renewal, and rarely values advice.
Which means losing that fight costs less than it appears. The traffic is expensive to obtain and the resulting customers churn quickly.
Where an agency has an advantage is anything requiring a person: situations that do not fit a standard form, coverage decisions somebody cannot make alone, and clients who need somebody to call when something goes wrong.
That is a smaller audience and a much better one, and it is almost entirely unserved because the whole sector's marketing is pointed at the quote.