It is safe to use a probe with less bandwidth than your oscilloscope. The probe acts like a lowpass filter so if you do use it to display a signal with greater bandwidth than the probe, the signal display will be degraded; e.g. a square wave will begin to look like more like a sine wave depending on the difference between the signal frequency and the probe bandwidth. Also, a low bandwidth probe may have more capacitance than a high bandwidth scope is designed for. That will make it difficult to compensate the probe and will also degrade the display. Unfortunately, probes rated to work with oscilloscopes having bandwidths on the order of 400 MHz can be rather expensive. However,it may pay to get one probe that can make full use of your oscilloscope's bandwidth and settle for less on the other probes. That will depend on the types of signals that you will be observing.
In a nutshell
Electricity is not supposed to flow through ground stakes in normal conditions. It doesn't mean its resistance is high, it's actually surprisingly small. That branch of the circuit is simply not closed normally.
In details
A ground is a reference point. You could litterally take any net in your circuit which is supposed to stay at a steady voltage and call it ground. After all voltage sources create a difference of potential (called a voltage) between two nets, regardless of what their potentials are - if they're both fixed externally, there will be a conflict and bad things, but if one of them is fixed the other potential will change accordingly. Generally the ground is taken such that we work with positive supplies predominantly, e.g. ground on the - terminal of a rectifier bridge. It doesn't mean all the current flow through that, it's only a reference.
The Earth has mainly a person protection role. No current is supposed to flow in the Earth because the actual supply circuit is isolated from the Earth, however what if this isolation is compromised (wires eaten by rabbits, children shoving their fingers in sockets...)? Everyone is indirectly connected to Earth (no isolation is perfect), which means that that circuit will now be closed and the only thing that will limit the current going through whatever is closing the circuit (e.g. people) is its internal resistance. Depending on the environment, that resistance can be sufficiently low to kill someone; refer to this thread about what voltages are considered safe. To prevent that, every enclosure is connected to Earth (a Earth-R-Earth circuit has a near-0A current), and the electric supply has a residual current device that compares the current going in and out, and cuts off the supply if there is a leak (through Earth).
The Earth is used for an equi[reference]potential supply The electricity provider needs to protect its people too, so the upstream supply is also referenced to Earth. Just like everywhere else. So what happens if the Earth is not a good conductor and its potential is not homogeneous? Users could be in contact with 2 different Earths, which can be a high difference of potential (=voltage). Thankfully, moist in dirt and water patches are good conductors, but above all the equivalent cross section of this fictive conductor is massive. Except during short upsets such as lightning, it has an excellent homogeneity in potential. Why use another conductor for ground which will use more copper and actually be less effective if we can use what's under our feet?
The Earth is also useful as a protection against lightning: lightning is just like any dielectric/isolator breakdown, it occurs where the resistance between the charged cloud and the Earth is minimal (see this amazing GIF). High trees, towers etc., and we can't risk relying on luck alone so highly conductive spikes are used to attract lightning, and the Earth is used to dissipate that energy. Loosely said. Normally lightning has enough current flowing to create through Earth and across human legs a voltage high enough to kill them, so it is spread out more evenly.
As usual, I'll warmly welcome anyone correcting me if not accurate.
Best Answer
Oscilloscopes usually require significant power and are physically big. Having a chassis that size, which would include exposed ground on the BNC connectors and the probe ground clips, floating would be dangerous.
If you have to look at waveforms in wall-powered equipment, it is generally much better to put the isolation transformer on that equipment instead of on the scope. Once the scope is connected, it provides a ground reference to that part of the circuit so other parts could then be at high ground-referenced voltages, which could be dangerous. However, you'll likely be more careful not to touch parts of the unit under test than the scope.
Scopes can also have other paths to ground that are easy to forget. For example, the scope on my bench usually has a permanent RS-232 connection to my computer. It would be easy to float the scope but forget about such things. The scope would actually not be floating. At best a fuse would pop when it is first connected to a wall powered unit under test in the wrong place.
Manufacturers could isolate the scope easily enough, but that probably opens them to liability problems. In general, bench equipment is not isolated but hand-held equipment is. If you really need to make isolated measurements often, you can get battery operated handheld scopes.