More than with a clean record. Carriers disagree most about flagged records, so the spread between quotes is wider. An independent broker can submit one record to several nonstandard carriers rather than you applying to each in turn.
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On a clean record, carrier pricing models converge and quotes cluster within a modest band. On a record carrying a serious violation, a lapse, and a filing requirement, the models diverge sharply because each carrier is making a different judgment about which of those factors predicts a claim. That divergence is the whole argument for comparison at this end of the market. The practical mechanics matter too. Applying to carriers one at a time by yourself is slow and produces quotes built from slightly different information each time, which makes them hard to compare. An independent broker appointed with several nonstandard carriers submits the same record to all of them and lays the results side by side. That is a description of how independent brokerage works, not a claim about any particular company or a promise about your result.