We expose the relevance of double occupancy conservation symmetry in application of the Hubbard-I approach to strongly correlated electron systems. We propose the utility of a composite method, viz. the Hubbard-I method in conjunction with strong coupling perturbation expansion, for studying systems violating the afore--mentioned symmetry. We support this novel approach by presenting a first successful Hubbard-I type calculation for the description of the metal-insulator Mott transition in a strongly correlated electron system with conserved double occupancies, which is a constrained Hubbard Hamiltonian equivalent to the Hubbard bond charge Hamiltonian with $X=t$. In particular, we obtain the phase diagram of this system for arbitrary fillings, including details of the Mott transition at half-filling. We also compare the Hubbard-I band--splitting Mott transition description with results obtained using the standard Gutzwiller Approximation (GA), and show that the two approximate approaches lead to qualitatively different results. In contrast to the GA applied to the system studied here, the Hubbard-I approach compares favourably with known exact results for the $d=1$ dimensional chain. ; Comment: This is the version submitted to Physica Status Solidi B. The final published version, taking into account Referee comments, is available exclusively from the publisher's website