Although US statutes and the CFRs authorize the issuance of Seamen’s Books, and refer to a USCG Form number, we have not had any seamen’s books for several decades. Apparently, the USCG screwed this up by policy— a long time ago. This puts US Mariners at a big disadvantage in the global employment marketplace.
Whether foreigners can enter the US without a visa depends on what country they are from. The US “Visa waiver program” applies to most countries. There is also the Global Entry System “Trusted Traveler” program that can be reciprocal with certain countries, including U.K. and The Netherlands among others. This requires a background check and a very clean record. It also costs time and money.
Shore leave for seamen is a different issue. I hear horror stories about the treatment of foreign, and sometimes US, sailors that want to go ashore in the US. It depends not only on the visa or citizenship status, but also the polices of the terminal operator. I do not have any firsthand experience with this.
US citizens have “visa free” travel privileges to all European countries, including the U.K. In fact, to most countries in the world.