RTS games have to keep track of exponentially more entities than an FPS. Destructive and dynamic cover in a game like Battlefield actually isn't all that demanding for a server because it's structured. You can't just destroy anything, and everything you can destroy is set up to be destroyed in certain ways. All the server needs to do is keep track of the destructible entities and their current states, then refer to those states when making hitbox calculations.
In an FPS, you rarely have more than 128 players in a single server (competitive games usually only have 10-20, depending on the title). That means the server only has to keep track of the locations of 128 entities, and calculate hitboxes on those entities. It also only has to send very limited player data, such as location and player action (firing, reloading, changing weapon, etc.). Even though FPS games usually run at a significantly higher tickrate than RTS games (CoH's simulation engine runs at around 8 ticks per second, compared to between 64 and 128 ticks per second for CS:GO games), it still uses significantly less bandwidth than an RTS that has to transmit location, health, entity, and action data for potentially hundreds of different units.
This is a big problem in a game like Starcraft where players often control over 100 units late in games. If both players had 100 units to command and the game was running at 8 ticks per second, the game would have to transmit and receive 1600 (100 units * 2 players * 8 ticks/second) units of information per second. Compare that to a 1v1 in CS:GO, where at 64 ticks/second the game would only have to transmit/receive 256 units of information (note for games like Battlefield, where the tickrate is far lower than that of Counter-Strike, the difference would be even greater).
That's 6.25x the bandwidth being used in the RTS compared to the FPS in order to accomodate the same number of players. Now if we look at things from the CoH perspective and use 15 or so units per player instead of the large numbers typical of traditional RTS games, we can get the bandwidth down to something approaching that of an FPS. However, we still have to consider the cost angle.
Dota 2 is structured very similar to an RTS, which makes sense considering it was originally an RTS mod. It was designed from the start to use client-server because it was designed first and foremost as a competitive game, and a competitive game that cannot gracefully handle disconnects makes running serious competitions an administrative nightmare. However, such architecture comes at a pretty steep monetary cost. Servers have to be globally located in order to accommodate people around the world, have to be maintained, and most importantly, have to be able to handle the immense bandwidth that a client-server game with large unit counts is going to produce. That last point is the most expensive, and one of the main reasons (along with having to recode most of their engine) why Relic will never adopt such a structure for CoH2. Maybe for CoH3, but even then it's unlikely.
Valve was willing to spend that money because they were trying to build a competitive game and a competitive community and knew they needed consistency if they were going to be taken seriously. Hell, they committed $1.6 million to a tournament prize pool before the game was even released to the public. Relic has neither the money nor the inclination to invest in something like that when it's seen as a luxury and not a necessity.
So no, building an RTS with a client-server model isn't impossible, especially if you have low unit counts like CoH does. But it's expensive, and in the case of CoH2 it would require a major rewrite of most of their codebase. In other words, it's completely impractical to hope for such a system to be implemented in CoH2.
If you're interested in reading more, I'd highly recommend this Gamasutra article by a Supreme Commander developer. Very enlightening on the challenges surrounding synchronization, message passing, and bug fixing in RTS games:
http://www.gamasutra.com/view/news/126022/Opinion_Synchronous_RTS_Engines_And_A_Tale_of_Desyncs.php
And another interesting article, this an academic piece on SC2's pseudo-client-server architecture:
http://choongsoo.info/docs/starcraft2.netgames12.pdf