Why are they silly? Someone wants to see that their property is in good order I think it's quite fair.
You're just borrowing it. Rejecting an inspection is a one way ticket to being given notice to leave as soon as the contract is up in my eyes!
It's a breach to your right of quiet enjoyment and privacy.
The lack of trust in this country is silly and mostly unwarranted.
Like I said, as a country, the UK is unusual in doing such inspections... it's weird.
Given your above example on rejecting inspection requests can't the landlord do the same if you reject the inspections that are written into a contract?
No, because it forms an "unfair term" so an argument like that taken to court to force an eviction will be rejected.
At the end of the contracted period however, the landlord would be within their right to serve notice and look for a new tenant.
Most of the places I've lived have been ok... current house we've been here over 9 months and thankfully no request for an inspection.
There was one however, they started demanding 3-monthly inspections and that was just frustrating... even going down the route of "it's ok, if you're not home we'll just let ourselves in"... ummm... no you won't... it ended up getting quite unpleasant and that was the initiating factor... oddly though, even though we had gone into a rolling monthly contract by that point - we were the ones to serve notice.
I'd maybe be OK with one per year, prior to contract renewal so they can have an informed decision as to whether they would like to continue renting the property to us... but even that is unusual compared to all the countries my family or I have lived in where they just don't do it... you pay your deposit and if it's not returned in the condition it was given to you, then it's deducted from that and you're potentially chased for any extra.