Not so.
FAR Part 91.205(d), Instrument Flight Rules, requires only that an aircraft approved for instrument flight have the following gyroscopic instruments - a gyroscopic rate of turn indicator, a slip-skid indicator, a gyroscopic pitch and bank indicator, and a gyroscopic direction indicator. The fact that various instruments are indeed based on separate power sources is because of industry standards, liability concerns, and common sense, not regulation.
Aircraft owners can alleviate concerns about a single source of electricity by installing (on some engines) a second alternator or (on some airframes) a wind-driven generator. If a wind-driven generator sounds archaic, remember that a number of corporate jets have them (they're hidden within the fuselage, to be deployed if needed), and many military jet fighters have wind-driven electrical and hydraulic generators. Installing a dual battery system to ensure adequate electrical power for avionics and gear and flaps (if applicable) in the event the aircraft electrical generating system fails is another option for single-engine night and IFR operations.
The failure of the only source of vacuum power has potentially serious consequences when flying in instrument meteorological conditions (IMC). Instrument pilots learn to cope with a vacuum pump failure by flying "partial panel" using the instruments powered by electricity (usually the turn coordinator) and nature (compass and altimeter). But flying partial panel in training and practice is very different, both physically and psychologically, than flying it in actual IMC.
Physically, flying partial panel in a training situation seldom lasts very long and is complicated by few, if any, associated problems. In the real world, you might be forced to fly partial panel for a considerable length of time (until reaching VFR conditions, for example), while also having to perform all of the normal IFR tasks such as coping with turbulence; finding, organizing, and reading charts; communicating with ATC; and flying the instrument approach. Besides that, you'd face other challenges, such as dealing with nervous passengers.
When flying partial panel in training we know, psychologically, that the situation is non-critical, and that we have two big advantages on our side - another pilot on board watching our every move, and VFR weather on the other side of the hood we're wearing.
One way to reduce the concern about relying on a single vacuum source is to install a standby vacuum system. You have several ways to approach this.
One option is to install an electrically powered standby vacuum kit. It's composed of an electric motor that powers a standard vacuum pump. The standby vacuum pump is connected to the aircraft vacuum system and can take over in the event of a complete engine failure, or failure of the engine-driven vacuum pump.
These systems work well but have several drawbacks. First, they are fairly expensive to purchase and install, and they can consume a significant amount of space on what may be an already crowded firewall. Also, they rely on the aircraft electrical system for power and, therefore, will be an electrical liability in the event of an aircraft generator, alternator, or engine failure.
Another type of standby system involves connecting the vacuum system to the engine intake manifold and using the manifold's reduced pressure to provide the vacuum to power the vacuum instruments. A check valve keeps the two systems separate. If the vacuum pump fails, the check value opens the vacuum line to the intake manifold. The amount of vacuum required to drive the instruments is low and won't affect engine operation adversely at cruise power settings. Unfortunately, this system won't be any help if the vacuum pump ceases to function because of a complete loss of engine power.
Although not popular in today's aircraft, another option for a standby vacuum source is a venturi. The venturi is a tapering metal tube with a narrow throat and an expanding-diameter exhaust that is mounted on the fuselage and connected to the vacuum system with an in-line switch (valve). It uses Bernoulli's principle to create vacuum. As the slipstream squeezes through the venturi's throat, its speed increases, and its pressure drops.
A venturi is quite reliable - unless it's blocked by something - such as ice. It takes airspeed for the system to work, so it isn't much good before takeoff. (But no prudent pilot would take off on a night or IFR flight with an inoperative engine-driven vacuum system, right?). The venturi is inexpensive and easy to install.
One alternative exists to installing a standby vacuum source. Install electrically powered standby flight instruments that duplicate the vacuum-powered ones. Naturally, this depends on available instrument panel space - and the owner's bank account. Compared to their vacuum counterparts, electric gyro instruments are quite expensive. They also tend to be heavier and need more space.
The solitary alternators and vacuum pumps that supply power to avionics and instruments in our single-engine airplanes are critical to our safety when we operate at night or in instrument conditions. Preparing yourself and your airplane for the potential loss of either of those components is time - and money - well spent.