These five schools have each had a 10-year cycle below .500 but only barely and, in Michigan's case, only one.
Tennessee:
The best 10 years for the Volunteers was 0.8548 from 1937-1946 while their worst were 0.496 for 2008-2017 and 2009-2018. Their helmet status gets questioned because there is an awful lot of mediocrity in their history.
Michigan:
The first thing that I want to point out here is that I think Bo Schembechler's achievements in Ann Arbor are often under-appreciated even by a lot of Michigan fans. IMHO, when Bo took over in 1969 Michigan was well on their way to becoming another Minnesota. From 1958-1967 the Wolverines were below .500 overall (0.4947, their worst cycle) and they hadn't been elite over a 10-year period in decades. Schembechler came in, took over, and took them to heights that few programs have ever seen (0.8553 in his first ten years from 1969-1978). Even Bo himself couldn't quite maintain THAT, but the program stayed close to or above 0.7500 all the way up until the RRod debacle.
LSU:
As I said above, I just don't think LSU is a helmet. In entering their records I noticed that their NC seasons just seem like complete out-of-the-wilderness flukes. They won the NC in 1958 but for the 10-years immediately prior to that (1948-1957) they were sub .500. That was their worst 10-year cycle (0.4762) but they were also below .500 the year prior to that and again in the 1990's. Their best ever was 0.8106 from 2003-2012. I don't think this adds up to the Tigers as a helmet. I think they are a generally pretty solid team that periodically jumps up and is phenomenal (1958, 2003, 2019) or phenomenally lucky (2007).
Alabama:
I was surprised in compiling this that for all of their soaring accomplishments at the high end, the Tide have had two significant valleys. They touched 0.500 in the 1950's (0.500 from 1949-1958) and fell below it not long ago (0.4811 from 1997-2006 and 0.4757 from 1998-2007). On the opposite side of things, their best (0.9071 from 2009-2018) is one of the four best 10-year cycles ever and they were also had peaks of 0.85+ in the 30's, 60's, and 70's.
Florida State:
This is the only school on the whole list that started playing football after 1927. Thus, the question for the Seminoles is how to evaluate their lack of history. For roughly the last four decades the Seminoles have clearly performed at a "helmet" level but prior to that their history is weak or nonexistent. Their best 10-year cycle was 0.8911 from 1991-2000 while their worst was 0.4660 from 1952-1961.