You can commute in a plane.
It all depends on what you mean by "commuting", or "flying on business".
This stuff ranges from trips which are absolutely critical (doing a formal customer visit; you
have to be there so a GA flight cannot be done unless the weather is assured) all the way through a broad spectrum, to trips which are really quite discretionary because the people you are seeing, or the conference/presentation/exhibition you are going to is not exactly life-critical. Customer visits are tricky anyway because generally you do not want the customer to discover you have a plane (obviously).
I think it is safe to say that if you want to do formal customer visits, or commuting to a 9-5 day job where you don't own the company, i.e. a 99%+ despatch rate, you need a de-iced plane, oxygen, an IR, the lot. Or balls made of solid brass but that is not a good long term weather strategy
Below that level, you can do quite a lot, but an instrument capability is still necessary. A purely VFR pilot who cannot go into IMC will be scrapping at least half his flights (if he has to go every day, all year).
I have met people who more or less commuted to some place of work but in all cases I know of they are in a pretty flexible situation where they can work from home if they can't fly, etc.
If you can go the day before or after, in the UK frontal weather pattern this dramatically improves the despatch rate. One person I flew with commuted from UK to Holland, flying home for the weekend - for years. If he couldn't depart for the UK on Friday evening he would go Saturday morning, etc. He had an IR.
I have done a lot of long trips across Europe and generally avoid flying through fronts (operating ceiling 20,000ft but no overall de-ice, or radar, so go for VMC on top enroute) but nearly always manage to get away on the planned date plus or minus 1 day.
Subject to the above, a light plane, IFR, works well for anywhere in France, or near Europe, and beats any other means of travel hands down. Forget the stupid naive rigged Top Gear car/plane comparison stunts. It even works within the UK, on certain routes like the SE to N Wales for example.