Really novice question here: if both the pilot and the aircraft are instrument-rated, why would anyone fly VFR? IFR lets one fly in a wider range of weather conditions and at night while there are no situations where VFR is allowed and IFR isn't. Or are there?
(This answer is based on light aircraft in the US.)
Leaving aside any scenarios where you must file IFR (class A, IMC) and any where you can't (pilot and/or aircraft not IFR-capable), it comes down to whether the 'overhead' and benefits of operating IFR are worth it for your particular flight. By the way, your question seems to assume that IFR is required at night, but night VFR is legal in many countries.
The 'overhead' of operating IFR is firstly in planning: there are different rules for fuel reserves, altitudes, airspace, alternate airports, weather minimums etc. Generally speaking you need more time and thought to prepare and file an IFR flight plan. Secondly, operating IFR potentially places a lot of restrictions on you: ATC can delay your takeoff, give you vectors that take you miles out of your direct route, put you in a hold, require position reports, and generally keep you busy. As a pilot, you have to perform at a 'higher' - or at least different - level.
For many people, that's already reason enough to file VFR if conditions allow (don't forget that in the US there's no need to talk to ATC at all on many flights). But the purpose of the flight is important too: IFR more or less assumes that you're flying from A to B on a fairly direct route. If you're training, or sightseeing, or dropping parachutists, or just flying around for the fun of it then IFR isn't really appropriate or useful. You can just get flight following instead, which gives you the benefits of ATC keeping an eye on you, without any of the IFR rules to follow.
And regarding your comment about IFR letting you fly in more weather conditions, there's a pilots' saying in the southern US (and probably many other places) that "if the weather's good, file IFR; if it's bad, file VFR". The reason is that Florida and other southern states get a lot of convective activity and it's very common to have to pick your way between thunderstorms and building cumulus towers to get where you're going, or just for a more comfortable ride. By remaining in visual conditions you're able to see what's going on with the clouds and being VFR means you're more or less free to change course and altitude as needed to avoid them. If you're IFR, ATC may put you in a cloud layer where you can't see anything and vector you closer to the buildups than you'd like. VFR just gives you a lot more options in general.
Finally, are there any scenarios where only VFR is allowed, even for IFR-capable flights? This might be different in different countries, but offhand I can't think of any in the US. IFR minimum altitudes are higher than VFR ones, so you can't fly IFR at 500' AGL, but I guess that's not really what you're thinking about. Maybe someone else will come up with something.
- VFR is the basics of flight. In VFR, you learn takeoffs, landings, turns, stalls etc., with plenty to visibility to help you recover should things go wrong.
- IFR flight puts more workload on the pilot.
- You won't want to fly aerobatics in IMC.
- IFR requires instruments. Instruments can fail.
- IFR requires more planning. You have to choose a route, tune VOR stations, join airways etc.
- Not all places have navigation radios on the ground. Many small airports don't have anything more than a grass strip and a few houses beside it.
- Sometimes you don't want to stay on predefined routes, for example in a search and rescue mission.
It is true that most commercial operations today are carried in IFR. However there are still plenty of other flights, such as private flights to a cousin's house, sight seeing tours, aerial photography, banner towing, gliding, parachuting, crop dusting, search and rescue etc., that are conducted in good visibility and require the pilots to navigate using visual references.
IFR would not be feasible for a lot of different types of recreational and professional flight activities.
For a majority of the flying that I used to do at one of my old jobs, I would not have been unable to get an IFR clearance had I wanted to. That notwithstanding, the routing would have been so complicated that it would have increased my workload—not to mention the controller's workload—to the extent that IFR would not have been feasible.
Many types of mountain flying would simply be impossible to do under IFR. The same goes for most ground proximity flying.
While not necessarily recommended, a pilot could fly VFR into an active MOA, whereas an IFR flight would not be cleared into that active MOA.
Regarding weather conditions, the fact is that I could legally fly in worse weather than would be allowable for many IFR operations, though to do so would—in some cases—be against company rules. It simply is not true that there are no situations in which IFR would be allowable where VFR would not.