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That really should not be the case at a domestic level. Whilst professional fees will often be based on a percentage of build costs, the fee proposal is normally a fixed sum up to eg RIBA stage 4 or 5. Budget is the first thing that should be nailed down.
Pushing for more expensive things during the design or build shouldn't affect their fees.If the client exercises their prerogative to change their minds (including value engineering bringing down the build cost) then additional fees are fair.
A bit late to the party, but with architects % of project cost, the major issue is that they have no incentive (in fact the complete opposite) to stick to the budget, so can often push for things that push the cost up. Obv not all will do this but you have to be VERY clear about budget and what you will accept/not accept, particularly if they are managing the job.