WARNING: Means of being less likely to die or to kill others is discussed below.
Reading may be considered useful..
Consider this "informed opinion" rather than holy writ.
In an oscilloscope you want the best result you can get for the money and it's far easier to build a single ended amplifier rather than a differential one when you want ruler flat gain for as much of the bandwidth as can be had and constant phase delay. An oscilloscope more often than not is required to measure a non sinusoidal signal, so it's ability to faithfully deal with the frequency components "across the range" is vital to it providing you an accurate picture of what is really there. In many cases single ended is good enough so they can give you dual earth referenced channels for more than a single differential channel but less to noticeably less than due differential channels.
Many better oscilloscopes have a dual channel subtract mode which gives you an approximation to a differential amplifier. The approximation is readily obvious in the ability to independently adjust channel gains so as to null common mode pedestal or to add in some component of it if desired.
People who "must have" true floating differential mode can buy the optional add on sure-to-be-dear differential module.
"Floating" an oscilloscope so that the local ground is not at true ground is a time honoured and usually somewhat frowned upon practice. In many cases it works well enough. The common practice in my (long ago) university days was to have a power plug with a pick-a-back socket. The plug had the earth pin cut off and said plug was usually coloured bright red in an attempt to forestall the various inevitable consequent events. For this to work the amplifiers must have been built single ended but floating with the scope ground wire the only connection to local (real) ground. This places this method in the same class as the one described in the question - the "1:1 transformer is substituted for by an isolated power supply. Where a smps is used for the mains supply (as will almost invariably be the case with equipment made at any time since Noah retired) then one may have to think about possible effects of X & Y capacitors connected between scope P&N and scope ground. These are isolated from true PNE by the 1:1 transformer but may still do interesting things to an attempt at emulating a proper balanced amplifier.
A BIG problem occurs (or can) when you try to be on your merry way probing various hot/neutral/earthed sources with no worries about a path to ground any longer using two channels at a time. Or trying to. The newfound freedom to use your probe tip + ground as Vin1-Vin2 does NOT extend to two channels where Vin2 is not the same for both channels. This is blindingly obvious either before you read this or as you do BUT the fact that you did not include it or note a caveat in your question shows how easy it is to overlook. Even if YOU are aware of this not so subtle limitation, it can still kill someone who uses your equipment or who works with you or who just happens to be physically in contact with the earth clip on channel 2 when you decide to connect channel 1 earth to phase. Obviously , a bit of common sense makes this practice safe [tm] for a rather more limited range of values of safe than most people are used to. Your local occupational safety inspector (names vary by country) or boss or small daughter may find the practice wanting.
All that said, most of us do things regularly as part of our workaday lives that are able to kill or maim us or others in a moment if we violate social contract or step outside acceptable agreed bounds of behaviour. Driving an automobile down a 2 lane road with oncoming traffic on the other side is a good example. Your car and your scope can kill you and others if used wrongly. Making really really really sure that the scope doesn't is a minimum requirement for playing the games that you describe, A floating isolation amplifier MAY be a better choice.