To say that the public don't believe that all is well in the RAF is being naive.
They know what they've been told in the mainstream media. Many of them aren't like us - they don't go looking at the REAL story, they don't encounter the military on a daily basis, they're not even vaguely aware of what the forces really do. Its all about boots on the ground in Afghanistan. They maybe see shiny red jets once a year and go Ooo. If they had a clue about the capabilities we've cut and are going to cut, and understood the real implications of it, then perhaps they'd take notice!! However nobody would take notice of the public anyway.
The Media aren't interested. They want gossip and glamour and scandal and sales. They don't want dull boring reality! The media have their own agenda, which may or may not match the political agenda or belief of the day, but certainly doesn't work in the public interest, or try to understand the REAL story. However cutting the Red Arrows would give them gossip and a "public interest" story that would get them a few more readers one day.
However they'll both be fed some nice polished politician who actually knows nothing and has no knowledge of their department, or of real life chasing their next expense claim and vote on the telly telling them it'll all be fine. They have some nice polished CGS/CAS/1st Sea Lord doing what they're told because thats their job and telling them that the services will cope like they always have and that its the right decision. The dissenters (I dunno, perhaps recently retired Admirals, Generals, Air Marshals, Security Ministers, etc - those who CAN now speak up) are dismissed as being out of touch (my arse they're out of touch!) and people believe it. You might even get a Defence Minister accidentally making it clear he thinks the cuts are going to far and that he DOES get it, and DOES understand the implications, but he gets spun and threatened back into line in fear of his career.
So why would the general public REALLY think anything differently?
Besides, they'll have a lot more to worry about when they get made redundant themselves and find the only "job" they can get is a voluntarily one running the council services they were getting paid to run 6 months beforehand. So maybe they don't actually even care... and nobody would take any notice of them anyway. Its been a long time since the polticians and the press actually gave a monkeys about who they're supposed to be representing!
So maybe binning the Red Arrows would make people sit up and take notice. My worry is that it might not have the effect we'd hope for!