The influence of the monomer chemical structure and architecture on polymer glass formation has been long appreciated to be dominated by two principal molecular factors, namely, cohesive energy and chain stiffness. Here, we utilize molecular dynamics simulation, along with the analytic generalized entropy theory (GET), to compare and contrast the role of cohesive energy in determining the thermodynamic and dynamic properties of polymer melts with and without bending constraints at zero pressure. As a general finding, our simulation results support the predictions of the GET that the temperature dependence of basic thermodynamic properties, such as the reduced thermal expansion coefficient and isothermal compressibility, becomes universal when the temperature is scaled by the cohesive energy parameter regardless of the bending constraints. Our simulation results confirm that dramatic changes in the temperature dependence of the structural relaxation time and extent of cooperative motion caused by cohesive interaction strength can likewise be eliminated largely using the same scaled temperature in polymer melts without bending constraints, but this simple picture does not emerge when bending constraints are introduced, a result in general accord with the predictions of the GET. Moreover, the fine features predicted by the GET, which are associated with the nonlinear growth of characteristic temperatures and the reduction of fragility with increasing cohesive interaction strength, are also confirmed by our simulations for polymer melts with bending constraints. Going beyond the validation of the predictions of the GET, we show that our simulation results for the structural relaxation time and extent of cooperative motion conform to the string model of glass formation in both polymer melts with and without bending constraints having variable cohesive interaction strength. We then utilize the string model to understand phenomenological models of structural relaxation of recent interest in glass-forming liquids. The string model also allows us to examine the dependence of the enthalpy and entropy of the high-temperature activation free energy on cohesive interaction strength. We emphasize the role of the activation entropy in improving the quantitative predictive capacity of the GET.