It is just a matter of taste: choosing what makes a balance simple or choosing to write a little longer balance equation.
The enthalpy can be related to other thermodynamic potentials.
It was probably defined to make things simpler. Try to re-write all the thermodynamics without the enthalpy or without the Gibbs free energy, you will see that some chapters will grow in page number and will be much less readable. That's all, I think.
When pressure is kept constant, work or heat can be accounted directly in terms of enthaply variations.
If pressure is not kept constant, you can still use enthalpy in the accounting but you will need to include not only the effect of work or heat but also the effect of pressure variation.