Why is the acylium ion stable?
The acylium ion is stabilized by the positive mesomeric effect of the lone pair of electrons on the oxygen atom onto the empty p-orbital of the $\ce{C+}$. This helps achieve octet completion of the carbon atom, and thus imparts stability to the carbocation.



(Image by Jü CC BY-SA 4.0, from Wikimedia Commons)

Resonance effects mostly dominate the weak inductive effect, so here the destabilizing negative inductive effect of oxygen atom has only a negligible role.

An alkyl carbocation has no such positive stabilizing mesomeric effect, rather only hyperconjugative effects, which are not able to provide as much stability as is possible in the acylium ion.