When you said that you worked on the LHC for several years - what was your role, and how were you involved with the vacuum system? Because your answers show a serious lack of understanding.
First, part tolerances are not a particularly important issue with engineering of high vacuum systems (sealing is effected by compression of gaskets, usually soft stainless steel gaskets for UHV systems).
Secondly, the difficulties in maintaining a large UHV system is usually related to "outgassing", from multiple surfaces and/or material imperfections, and are rarely due to "a single flaw in one part".
Thirdly, you are using the word "exponentially" wrong, even in the context of your flawed claim which is addressed below.
Finally: "the force on the pipe" is not, in a meaningful sense, proportional to the square of the radius. The forces in the pipe wall are proportional directly to the radius (formula is stress=pressure*radius/thickness), if it was otherwise pipe thickness would grow as the square of diameter and large pressurised pipes would be physically impossible.
Happy to do the math for you when you need it, best to leave it to the experts.