They won't get blown up on turn one. Mech Eldar generally don't start on the table ever
Seriously though, mech Eldar do as much damage as possible in as little turns as possible. That's why units like 10 warlock, or 10 fire dragons or yriel work great.
They reduce incoming fire by playing less turns. Plus you pick up a huge deployment advantage and concentration of force advantage.
As for the fire dragons... First of all they are less than 300 points tooled out and that includes the transport. And if you blow up the transport at the first opportunity they are usually already 24" on the board (or more with star engines).... But yes. Tanks die. Troops get stranded.
Remember fire dragons fleet and have melta bombs. Most people forget this when they ignore them. This is yet another situation where 10 is a lot better. Your bound to get some hits even on vehicles movign more than 6.
What usually happens is that you are close enough to the transport you were hunting. The enemy then unloads the squad out of the transport and trashes the firedragons.
Which is great as you can then you go torch the squad that you were trying to get to in the first place.
If they ignore you and you have no target, you go to ground and hide for a 3+I, and you can play taxi transport with another unit's ride.
But yes. You get the point. With Eldar you nuke a unit and then go hide or zoom away.
Eldar are a thinking man's army. You simply will never do things like clear 200 orks for a massacre, but you can kill an entire half of an army in a turn or two if things work out right, which might be enough to give you a win.
Worst case scenario you can generally spam the crap out of objectives for the draw.
Pete