1) How often will you actually change gateways? I can tell that we have had the same gateway account for 7 years and processing millions of dollars a year and changed merchant accounts many times. The gateway industry is pretty much a commodity, very little price change, no difference between gateways so there is not much value in changing. There are reasons you might change merchant accounts as rates do change and volume can make a difference.
2) How to change. If you really do need to change gateways and keep in mind Authorize.net is not going out of business so that is not a consideration, think about the right way to do it. I would either slowly move accounts over as operations like CC updates happened or run multiple gateway accounts to diversify risk.
3) Where is the risk? The largest gateways are not going anywhere so your real risk with not doing billing on your own is the billing provider. And yes I am saying this and I am a co-founder at Chargify. Would you prefer to have your CC details held there or at a gateway where you can always access the token to make future charges? This gives you the ability to move billing providers compared with getting locked in.
At Chargify we take security very serious and have reviewed all of the different reasons around this topic and can tell you that today all CCs are stored at the gateway but in the future we will have an option that gives YOU the choice where to store this data and how.