I had a different experience with the taxis at plaza athenee and I don't want potential guests to be too concerned. When you tell the doorman that you want a taxi, they wave one down on Wireless Road and it pulls in to the Hotel (we are talking only 100 yards). They will get you a taxi as fast as if you could hail one yourself - any taxi willing to charge the meter rate is going to pull in, you will only miss the ones that would overchage you. I used a taxi 3 times - the skytrain is so convenient - and only waited longer than 30 seconds once because there were 2 people waiting ahead of me.
Regarding a taxi to the airport, that is a different story in Bangkok. The low pricing to the airport is often a complaint from the taxi drivers and they often do not wish to take the fare. It is not the hotel's fault if the taxi driver drives up and chooses not to take you. What is unfortunate is when the taxi driver agrees to take you and then tries to charge more (this happened to me at the WGS, but not at the plaza athenee). Catching taxis that take you to the airport with the meter are difficult all over Bangkok and you often have to go through 2 or 3 to find one. I generously tip when I do not have to fight the taxi driver because it is good to encourage the "correct" behavior.
Most importantly, the fear factor of being overcharged is greatly exaggerated by new visitors. If the taxi turns on the meter (and you should insist on this), then you are usually safe. If not, you can negotiate the flat rate and risk them overcharging you, but you could almost always get a 300-400 baht flat rate to the airport at worst. This is about $9-12 to the airport and can be overcharging you by as much as $5, but usually closer to $2. Not fun, but if you are staying at these nice hotels, it is a shame to let it ruin your time. I recommend waiting to get the honest taxi drivers which should not take too long, but I understand that sometimes there is a plane to catch.