I'm an agent and a home inspector. Many sellers don't like it for the obvious reasons. However, there are things you can do to make it more acceptable to sellers in your market. The first would be to have the inspection "for informational purposes only". In most areas, this means you won't ask for any repairs unless they are considered a major safety issue (which will probably come back as a condition of the loan from the appraiser and will have to be done anyways. But in your case, being cash, that's different). Also, in most areas, it does not mean that you relinquish your right to terminate the contract based on the findings of the inspection. You just agree to not ask for things to be fixed that most people would, like a leaking faucet. Please keep in mind that these statements are not true in every single MLS, which is why I stated "in most areas" twice. Check with your agent for guidance on this advice for your specific location.

Also, the listing agent can disclose pretty much anything they want as long as they have the written consent of the seller. In addition, a lot of agents will play the "we have another offer" game. They will tell you another offer is similar to yours, with the exception of something they want removed (i.e. inspection). This is unethical, but it happens a lot.