The phrase "almost unfettered access" is correct and usable in written English.
It can be used to describe a situation where access is nearly unrestricted, but there may be some minor limitations.
Example: "The researchers were granted almost unfettered access to the archives, allowing them to explore a wealth of information."
Alternatives: "nearly unrestricted access" or "practically unlimited access".
When big corporations had almost unfettered access to credit, they could play one off against another for the cheapest loans.
As the New York Times reported, the court "made it clear that American intelligence agencies had almost unfettered access to the data, infringing on Europeans' rights to privacy".
It was the first of several tussles between the two, and a shock to the system for Trump, who had grown used to softball questions from TV journalists, at Fox News and other networks – all of which have given the billionaire almost unfettered access to their airwaves in the knowledge that he immediately boosts their ratings.
That's because while ICE has almost unfettered access to courthouses nationwide, the agency's reach into Rikers Island is extremely limited.
Four years ago Poitras decided upon Julian Assange as a subject, and managed to gain the WikiLeaks founder's trust to the extent that he allowed her almost unfettered access to his day-to-day activities before and during his prolonged stay in London's Ecuadorian embassy.
And it's even more disturbing that big businesses -- which the Supreme Court ruled in 2010 have a right to "free speech" in bankrolling election campaigns -- can also have almost unfettered access to our personal space so they can target each of us more effectively for market exploitation than a drone command center can target the Taliban.
Iranian officials have nearly unfettered access to Mr. Karzai's palace, bypassing the normal rules of protocol.
This was timely as U.S. Route 101, which would soon provide nearly unfettered access to the trees, was under construction.
A "master key" that could give cyber-thieves unfettered access to almost any Android phone has been discovered by security research firm BlueBox.
Mr. Tifatul uses Twitter to communicate with Indonesians almost every day, but harbors misgivings about an American-style, unfettered access to the Internet.
A1 Inspectors Seek Wider Access United Nations weapons inspectors used their first meeting with Iraqi officials in almost four years to press for unfettered access to sensitive sites like the offices of Saddam Hussein's Republican Guard.
