My View is any "Rush" to top tier tech is incredibly risky and more or less an all in.
Your game plan should include having these Top Tier units in your composition, but to cut corners by building cannons for defense or skipping gateway units, 1 basing because you cant cover 2 bases, just to get mass carriers is a mistake imo.
As Zerg my end game plan against T/P is to get Broodlords, quite frankly I need them to deal with 99% of the Terran and Protoss Army compositions and/or Turtleing I may encounter.
But to get there I build the following units; lings, hydras, roaches, lurkers, mutas corruptors (more or less in that order) and occasionally blings if the enemy unit composition means blings will help. I also spend a fair bit on Tech for these units and expand like mad (I need a min of 3 mining bases for Broodlords)
By that time assuming the enemy has not turtled up I will have had a few fights and hopefully my army will still be in good shape, so I will contain him whilst the Corruptors get into position and morph into BLs. Once I have 6+ BLs and a bunch of Hydras/Mutas + 4+ corruptors I know that my army will be able to handle anything an enemy throws at me.
If I was Toss I would want 6+ carriers in my Army Composition, but in order to get them I think I would need 3-4 mining bases and I would have to make those carriers all in one hit (i.e. 6 Stargates) In order to have that amount of bases I would need the ground/Air Army to protect my bases. Which means I would probably already be in the position to win the game, and the carriers are just for ***** and giggles.
VR Rushes are (or were) so common place (especially against Zerg) that I think Zerg more or less figured out how to counter them, and the counter (fast hydras + 2-3 extra queens) basically put Zerg in a good position to hold almost anything that Toss can send by that point in the game. Meaning Zerg can flesh out his army with other units and keep toss at bay for the remainder of the game, until Broodlords can be made (if the game lasts that long)