Why is a cationic trialkylammonium functional group inductively withdrawing in nature? The alkyl groups on the nitrogen ion should donate electrons (alkyl groups are electron donating in nature). So, irrespective of the nitrogen ion being a cation (which is an electrophile), the alkyl groups should compensate the electrophilicity of the nitrogen cation, and the ion as a whole should be electron donating in nature.

Then why is $\ce{R3N+}$ considered to be electron withdrawing?
Nitrogen is a very electronegative element and the fact that nitrogen bears a positive charge in the ammonium ion makes it even more electrophilic(as you pointed out) . Alkyl groups are only weak electron donating groups and can't help much about nitrogen's positive charge.Hence the ammonium cation is inductively withdrawing in nature.