Good Morning KTC!
It's fifty years since law school so you will forgive me for not being more concise.
Immunity from prosecution can be granted by a grand jury or a legislature.
The Fifth Amendment is something that you must invoke.
There is a profound and significant difference.
After immunity is granted, there arises the ability to compel testimony under certain circumstances.
The text of the Amendment--
"No person shall be held to answer for a capital, or otherwise infamous crime, unless on a presentment or indictment of a grand jury, except in cases arising in the land or naval forces, or in the militia, when in actual service in time of war or public danger; nor shall any person be subject for the same offense to be twice put in jeopardy of life or limb; nor shall be compelled in any criminal case to be a witness against himself, nor be deprived of life, liberty, or property, without due process of law; nor shall private property be taken for public use, without just compensation."
So, "of course they don't".
Immunity is not conferred by the assertion of your 5th Amendment rights.
Transactional immunity does not arise from the 5th.
Use/derivative immunity does not derive from the 5th.
The results can seem quite similar, although they are not.
Invoking the 5th Amendment is not a self grant of self immunity. Invoke the 5th Amendment and there is no ban from further prosecution. Invoke the 5th and you are immune from nothing.
After invoking the 5th Amendment there is no immunity.
There is nothing. There is no assumption of guilt.
You can sit there and invoke the 5th Amendment all you want. It grants you absolutely no immunity.