Your reluctance to answer the hypothetical question on a member of your family being falsely accused is very telling. For the most part, no family want to think their own are capable of it. Worse so when it is clear they are innocent.
So on Visiting Day, Will you visit the local nonce prison and tell eg Dad that I'm sorry but you were just collateral damage. But at least it was another conviction.
As PP have pointed out. Numbers given for reported cases without conviction, although deeply disturbing and extremely upsetting for those genuine victims to not get closure, Cannot be reliably used to state how many do not receive justice.
Have you a link that shows the conviction rate from 2009 until today. The years 2019-2023 and perhaps beyond, Will not show a proper representative figure, due to the reduced element of interpersonal interaction with covid. Add that to a much reduced Court system during that period a number of cases that would have been included did not take place.
I don't think the majority of us feel that someone accusing another of rape is lying. It is up to the courts to make the decison of who's version of events is more likely.
A couple of your suggestions I'd like to reply to.
inquisitorial rather than adversarial prosecution. That means working to establish the truth rather than "guilty/innocent".
If truth is established beyond reasonable doubt, then a conviction takes place. Anything less is not acceptable in law.
additional crime of reckless penetration that focuses on whether the man took appropriate steps to ensure he had consent.
I believe that is part of the investigation and trial process as it is. A good example of this is having sex with a woman under the influence. Was she able to give consent. If the answer is found to be no in court, then he gets a conviction.
The Swedish system although sounds good to a certain extent. What it is essentially saying is that despite there being no consent on the victims part, because the intention of the rapist was not to rape, but just to have sex. Then that is reducing the severity of what was carried out. Sex without consent is Rape. No matter how you dress it.
altering the "reasonable belief of consent" clause or making it so certain things can't be given as reasonable belief. Such as, being so drunk you don't know who you are fucking. Or having very rough sex with a 16 year old believing she consents, when you are 30
Part of my answer to this is given above. Having rough sex with anyone, be they 16 or 60 makes no difference. The important part is consent.
Sadly the under-reporting of crime of all kinds is increasing. Due to lack of police & courts. Many feel it pointless as they know the police will not investigate low level crime now. Where this is going to lead is frightening imo.