Austria, in any case, was in decline. Friedrich Schiller's then relatively recent play William Tell would have refreshed memories about Swiss non-acceptance of Habsburg rule.

The Helvetic Republic was actually a product of the French revolutionaries. Napoleon sort of reverted part of it in the Act of Mediation as local insurrections had been going on against the French revolutionary ideas in rural Switzerland. Indirect control (by money and culture), as practised by the French kings and again Napoleon, was a lot smarter than any costly occupation.

De facto, Switzerland had been a quasi-client state of France (thanks to French payments). The split into Swiss Protestants and Catholics meant that Switzerland lived for 200 years in a state of internal cold war but kept out of foreign wars (except as a supplier of mercenary soldiers).

Swiss neutrality post 1815 thus was a net loss of a client-state for France (as was the integration of Belgium into the Kingdom of the Netherlands). Overall, Switzerland was of little importance to the Great Powers. Neutrality was an excellent and cheap solution that removed this central area from play for any Great Power.