3 weeks is nothing to wait when selling/buying a house, however, there's usually nothing stopping an engineer doing a survey during this time, the engineer will then usually advise if there is any documentation required from the vendors solicitor (e.g. cert of compliance, or issues around the plot), so it's odd that your solicitor was the block here, but maybe there is something special about the house that's not being called out here that made your solicitor add this condition (you also need to keep the selling estate agent aware of all these items, as they will be talking to the vendor directly and will make them nervous about delays).
Do the vendor know you're worried about subsidence? Be up front, and tell them what the inspection is for, make sure the EA knows (they'll dread this as they'll have to put it back on the market with a question mark around subsidence).
Is the house detached? If it is attached to the neighbour, and the neighbour has subsidence, you need to run away fast.
It does sound like there's some naivety on your part, which can be understandable if it's a first purchase, be up front with issues, don't try and scrimp and save on what's required to buy the property (some beginners balk at the idea of getting a survey done before signing contracts in case they "lose" the money, this is a big red flag to any selling EA), the key is to keep everyone fully informed at all stages, and flag when and why decisions get made.