Indeed, alkyl length increases the acid strength (conjugate acids like protonated amines, included) and decreases the basicity of bases, due to the positive induction effect.
But in case of dialkylaminoethyl ethers cleavage, the problem is also kinetic because it is a consecutive reactions route that follows three steps.
1). Ionization of the hydracid but this is instant and doesn’t count in reaction kinetics.
2). Protonation of the oxygen atom, which is also fast but reversible.
3). Attack of the halogen anion to the carbon that is in α-position of the protonated oxygen.
Already, amine group consumes one molecule of the hydracid and decreases the protons concentration.
But this is not all. Hydracids are strong acids with negative pka and thus, Henderson-Hasselbach equation is not applicable. So, the protons concentration must be calculated by taking into account the acid dissociation, as well as the water auto-ionization and the protonated amine ionization; which means that the concentration of halogen anions that attack to the diprotonated dialkylaminoethyl ether, is quite lower than the protons concentration, whatever that means to the overall reaction kinetics.
In other words, dialkylaminoethyl ethers cleavage is quite slow and needs more heat than usual, in order to be adequately accelerated.