Reactivity of Alkanes, Alkenes, and Alkynes
Maybe it will help if you look at reactivity in terms of ability to attract electrons instead of bond enthalpies. Alkanes are $sp^3$ hybridized, and hence have $25$% $s$ orbital character and $75$% p character. $s$ orbitals are closer to the nucleus and thus have a 'contracting' effect on the hybrid orbital. Greater the $s$ character, 'smaller' the hybrid orbital. This means that electrons are more closely packed. Alkanes have only 25% $s$ character, hence the hybrid orbitals are comparatively larger, and the effective nuclear charge on outermost electrons is less. Alkenes ($sp^2$) and alkynes ($sp$) have 33.3% and 50% $s$ character respectively. Thus their hybrid orbitals are SMALLER; i.e. effective nuclear charge is more. This means that it is easier to accept electrons, as now the effective strength of nucleus is more. Hence, alkynes can easily accept electrons, followed by alkenes and then alkanes. Thus, alkynes are most reactive, followed by alkenes and alkanes. Even though increase in $s$ character increases bond enthalpy, but it also increases the electron withdrawing capacity; and it is the latter which predominates. 

(In fact, in general, greater the $s$ character, more the electronegativity and more the acidic nature).