When used properly, the Anvil Churchill seems to be in a decent spot, price-to-performance-wise.
Just like most damage-sponge-oriented Tanks, the Churchill has to be used cautiously at first, until it can vet up. Once the Churchill has reached Vet3, and receives its much needed mobility buffs, it can be used much more aggressively to spearhead your attacks.
The problem, however, is that unlike other damage-sponges (which rely on high armour), the Churchill trades-off a significant amount of armour for the biggest HP pool in the game.
The benefits of a high HP pool (with low armour)
The Churchill has the following advantages over high-armour medium-HP damage-sponges: wearing down the Churchill's HP pool is more consistent (and less RNG dependent). This might seem like a downside at first. However, it allows the UKF player to predict how much damage the Churchill is able to take before it has to be pulled back.
Compare this to the IS-2, for instance; a bad RNG-streak can easily ruin your day.
Finally, the enormous HP pool is the biggest middle finger to flanking the Churchill (which isn't difficult to achieve, given its lack of mobility).
Edited to add (8 March): A higher-HP-to-armour ratio (for the same HP * armour factor) also makes the Churchill MORE resilient to attacks that cause deflection damage (e.g., Panzerschrecks). Even if Schrecks don't penetrate, they still cause a fixed amount of damage; in a blob, deflection damage can become significant. (I'm not even taking flanking into account here).
The downsides of low armour
Just like most damage-sponges, a Vet0 Churchill is not immediately useful to spearhead a big attack. In order to unlock its full potential, it needs to attain some veterancy. This will yield the necessary mobility (and crit-damage repairs at Vet3).
However, the low armour and low speed of the Churchill has a fatal downside; the Churchill takes a lot of damage from just about any source. This makes it act as a Veterancy pinata to the opposition. Given that the Churchill cannot finish off enemy targets, the enemy veterancy will accumulate (enemy tank destroyer, paks, etc).
Thus, as the game drags on, it is very likely that summoning a Churchill will end up doing more harm than good to the player (even if the player plays cautiously and manages to preserve the Churchill)
(Of course, the other downside is that you need to spend more time repairing the Churchill. However, Anvil comes with Heavy Sappers, so there's no issue there)
Edited to add (8 March): Another downside is that Churchill has a predictable performance. Just like the Churchill user knows when the tank has had enough and needs to be pulled back, an attacker will also be able to tell whether a flank (trade) will succeed or not. Low-armour contributes to eliminating RNG to the attacker's favour in this situation.
A modest proposal: just reduce awarded veterancy to attackers
A higher-armour Churchill would "bleed" less veterancy to the opposition. However, a higher-armour Churchill with a 1400 HP-pool would be completely OP for its price. Instead, we could just tweak the awarded-veterancy modifier. That way the Churchill will perform on a similar level to other damage sponges with respect to the veterancy-pinata aspect.
The modifier could be something along the lines of -30% awarded veterancy (which would be similar to the Churchill having 340-ish armour).