it was said before that the change of the direktion horizontal vers vertical cost an extra portion energie.... so the calculation was not much/exact valid it was under a limit value view, and yes it is possible to climb with an bird and change Ekin into Epot... (in detail the pressure on the water-surface deep under the bird has to rise a little bit, and the earth will change her position on her way round the sun also a liiiiitle bit)
a calculation just to control the plausibility of datas
and due to the lots of lessknown faktors (AoA, Cl, Cd, Cm, temp. density, spezific weight, reynold.....) it is just a practician desicion of the calculator if he will more talk over the marginal conditions or over the basic applications
and yes the used calculations of Ekin has some mistake in turbulence conditions with changes in the airspeed, this mostly cost a second portion of energie....