When the thickness is reduced to nanometer scale, freestanding high molecular weight polymer thin films undergo large reduction of degree of cooperativity and coupling parameter n in the Coupling Model (CM). The finite-size effect together with the surfaces with high mobility make the α-relaxation time of the polymer in nanoconfinement, τ(α)(nano)(T), much shorter than τ(α)(bulk)(T) in the bulk. The consequence is avoidance of vitrification at and below the bulk glass transition temperature, T(g)(bulk), on cooling, and the freestanding polymer thin film remains at thermodynamic equilibrium at temperatures below T(g)(bulk). Molecular dynamics simulations have shown that the specific volume of the freestanding film is the same as the bulk glass-former at equilibrium at the same temperatures. Extreme nanoconfinement renders total or almost total removal of cooperativity of the α-relaxation, and τ(α)(nano)(T) becomes the same or almost the same as the JG β-relaxation time τ(β)(bulk)(T) of the bulk glass-former at equilibrium and at temperatures below T(g)(bulk). Taking advantage of being able to obtain τ(β)(bulk)(T) at equilibrium density below T(g)(bulk) by extreme nanoconfinement of the freestanding films, and using the CM relation between τ(α)(bulk)(T) and τ(β)(bulk)(T), we conclude that the Vogel-Fulcher-Tammann-Hesse (VFTH) dependence of τ(α)(bulk)(T) cannot hold for glass-formers in equilibrium at temperatures significantly below T(g)(bulk). In addition, τ(α)(bulk)(T) does not diverge at the Vogel temperature, T₀, as suggested by the VFTH-dependence and predicted by some theories of glass transition. Instead, τ(α)(bulk)(T) of the glass-former at equilibrium has a much weaker temperature dependence than the VFTH-dependence at temperature below T(g)(bulk) and even below T₀. This conclusion from our analysis is consistent with the temperature dependence of τ(α)(bulk)(T) found experimentally in polymers aged long enough time to attain the equilibrium state at various temperatures below T(g)(bulk).