I think we all agree that you need a very high bandwidth scope to look at fast glitch pulses in sufficient accuracy.
The question though is if you really need to do that.
If you look at fault injection from a scientific perspective, the answer is likely "yes". You would need a HF signal chain, a very fast signal generator, impedance-controlled power lines to all make this reproducible. It'll be significant effort to just characterize everything - starting from measuring capacitance, your FET's Rdson, your power rail effective series resistance etc.
But if you "just want to get the job done", you don't need any of this. Instead you just try - if the DUT crashes, you've glitched too long/strong. If the DUT doesn't react to your glitch, you make the glitch longer or improve fall times. Within a few iterations you will likely get something that in practice works as well as a "scientific glitch", except that you can't fully characterize it and it probably significantly depends on external factors (such as temperature, cable properties etc). But in many practical scenarios ("I want to get this global key") all of this doesn't matter, since the attack only has to work once.
For SCA, it's very similar. There are scientific papers that can extract an AES key from a double-digit number of traces. They use high-quality differential probes, shielded environments and months of setup cost. But then in practice you can just take 100x as many samples (still very viable in most scenarios), do a little bit of post-processing like rejecting bad quality traces (for example where there was a lot of random interference, like someone switching on a light), and still get the key. No need for a differential probe if you just sample the power rail on the high side with an offset (which most/all scopes can do).
Really the best here is to get a lot of practice, and you can do that with cheap scopes. Paul Kocher did his first power analysis using an analog oscilloscope, watching the "square"/"multiple" pulses of a smartcard RSA implementation.
Once you run into real limitations, you could then invest in the right set of equipment. Or - and that's not a bad choices either, but it depends on your financial capacity - you throw a lot of money at the problem, and see what sticks. The latter option is not even a bad strategy, especially for companies, where just a few hour of engineering works equals to a nice scope.
For the record, I've did most of my DPA work on a Tek DPO4034 and later a Tek DPO5034. But back in the days there weren't budget alternatives for large sample depth.
Also to add: For SCA, at some point the bottleneck is the rate at which samples can be processed, so you need to limit either a.) # traces, b.) Samplerate/Bandwidth or c.) duration.
Duration is usually fixed through the region that has the secret operation. Eventually my observation is that higher #traces brings more benefits than higher bandwidth. So for many scenarios you can get away with just a few samples per clock transition, so unless you're doing SCA on multi-100MHz devices, a 100MHz scope should be fully sufficient.
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