Whatever happens, the solar day stays the same. Time zones actually break the solar day. Freed from the constraints of time zones the solar day becomes its own thing. DST is just an ugly hack piled on top of the mess time zones created in an attempt to go back a ways to solar time.
No, DST has nothing at all to do with solar time. It's a hack alright, but it's not fixing any problem introduced by time zones.
The first letter of DST stands for "Daylight". In the world before time zones people basically used three references based on sun position, sun rise, sun set and noon. The introduction of time zones decoupled noon from the time when the sun was at the highest and was part of the process that led to people doing things by the clock and not the sun. Because sun rise and set vary with respect to time zone time DST was an attempt to partially allow people to just start doing things when the sun came up.
Perhaps the writing is silly, but there's nothing silly about the point the point that of course people will maintain the solar day for daily life, and abolishing timezones will basically break time for most people (especially those whose "midnight" (and so the changing of the date and name of day) will land during the solar day).