A brief web search suggests that aviation would have no benefit or disadvantage from either regular clock changes or their abolition – at least when it comes to reporting time itself.
This is because aviation generally uses 'Zulu time' – a.k.a. UTC for all communications except for the departure and arrivals boards that are displayed directly to passengers using local time. The AOPA (Aircraft Owners and Pilots Association) writes:
Greenwich Mean Time (GMT) is international time, the basis of the world time clock. It helps eliminate confusion across multiple time zones. It is also known as UTC (Coordinated Universal Time). Aviators commonly refer to it as Zulu time.
Aviators use this worldwide, 24-hour time to eliminate confusion about "a.m." and "p.m." and different time zones. It makes time comparisons and conversions easier.
There has been a question over at Aviation.SE asking about the reasons for using Zulu time in aviation which user Casey answered:
If you are flying along the border between Arizona and New Mexico in the summer and given a hold:
Cessna 1234 hold at FIX, right turns, 10 mile legs, expect further clearance at 1630, time now 1602
If that were local time, you'd have to now determine if that fix is over AZ or NM, because NM observes daylight saving time and is in MDT/-0600 and AZ does not observe daylight saving time and is in MST/-0700. This is a needless check that is distracting and can cause confusion all due to using a local time. Instead, we know the times given are Z/UTC time and "1630" has an unambiguous meaning no matter where on earth our plane is located.
As this approach completely nullifies any effect that clock changing might have on schedules and such, the local time will have zero influence on aviation.
On the other hand, for long-distance flights that cover two different DST areas – e.g. transatlantic flights where European and US clock changes are not synced or flights from Europe to East Asia where DST is not observed at all – the clock changes cause scheduling problems. Namely: In which time zone does the airline wish to keep its departure/arrival time constant and are there slots available at the respective airport. Summarised well by CrankyFlier:
That’s easy enough, but the international world makes it a lot harder. You always have this problem when traveling between the northern and southern hemispheres since the seasons are reversed. Right now, for example, LA and Auckland are only three hours apart, but in March when the US springs forward and New Zealand falls back, the difference will be five hours. Most of Asia does not have Daylight Saving Time either, so twice a year, they see times shifting as well.
But this year is a special kind of year since the US changed when it observes Daylight Saving Time. See, until now, the US and the EU changed clocks on the same date, so everything was fine. [EDIT 11/6 @ 847a: I was wrong, there used to actually be a one week lag in the Spring, so this year it has just expanded in size.] But this year the US moved Daylight Saving up a couple of weeks in March and back a week in October/November, so now there are a few weeks, including last week, where times are really messed up in the extremely busy transatlantic market.
At most airports, that’s no big deal, because there’s room to move. But at congested airports like London/Heathrow or Frankfurt, the airlines don’t have slot flexibility so I assumed they’d have to just change around their flights in the US. But what about when that involves flights at New York/JFK or Chicago/O’Hare, also congested airports? This gets very tricky and the result is a hodgepodge of schedule changes for some airlines.
Taking a random example, I looked up the flight data for JL 408 (Japan Airlines flight from Frankfurt to Tokyo-Narita) on Flightradar24 and noticed that its departure time in Frankfurt remained the same but its arrival time in Japan shifted back by an hour, reflecting the fact that its 19:40 local departure time used to be 17:40 UTC but has been 18:40 UTC since Sunday.
Taken together, I fail to see any advantage that aviation has by changing the clocks.
(The answer may vary for general aviation, but its effect should be exceedingly small so I decided to disregard it.)