Mains voltage is full of transients, and any one pulse has enough energy to destroy a TVS diode.
At the very least, you need a fuse in front of the diode, so when it fails shorted, it doesn't continue to draw short-circuit current. (Diodes normally fail shorted, at least until they've absorbed enough current, as a short, to get physically blown open. Often with a burst of flame, flying debris, and wailing and gnashing of teeth...)
Surges are a random thing, and it varies with country, region, and time of year. You're more likely to get nasty surges during thunderstorms -- though they can be carried in from distant strikes, too, not just what's over your head. You're more likely to get surges in areas with overhead wiring (as is the case in much of the U.S.), versus buried / underground wiring (which is more resistant to lightning strike). And still more likely to get surges in areas with poor power quality: frequent dips, interruptions, short circuits, etc., typical of many countries with poor infrastructure.
Over some years, you're very likely to get at least one hit, even in a "quiet" area. That's your basic time frame as far as "need". If it needs to be reliable over years, it needs to withstand transients.
If you need protection, a MOV is better: these components are capable of handling the energy. They still aren't really rated for it, in the sense of: a mains surge simply delivers so much power (peak power in the megawatts), that a protection device must be absolutely massive to withstand it forever. So, they wear, and don't last forever. You still need a fuse to protect against failure. But you can take a product that won't survive one surge, to one that'll last a decade or more.
But best of all, that pesky transformer you have, solves pretty much all.
I repeat again, my opening comment: do you know you need one?
Because I'm betting either, you don't know whether you need one at all, or you don't need one, because it's already fine!
An iron cored power transformer has three things going for it:
1. The winding resistance significantly reduces the surge energy available on the secondary side. That is, you might start with a fuck-off-massive 2.5kV surge on the primary side (carrying some megawatts of peak power), but most of that disappears across primary winding resistance (~100s ohms for this case, so the worst-case power can only be ~100s kW unless something sparks).
2. The high voltage rapidly saturates the transformer core, shunting much of the energy away from the secondary. Instead of a ~ms long surge, it's truncated to a bit under 1ms, worst case. That cuts the energy in half, at least.
3. Thanks to leakage and secondary DCR, the impedance at the secondary is even higher still (well, adjusted for turns ratio). This means that, if you still need transient protection, you stand an absolutely realistic chance of succeeding, by simply placing, say, a 1.5KE12 or SMDJ12A, across the FWB output. Such a diode is good for ~kW of surge, which is about all that you need to deal with, after passing it through a transformer.
But even better than that, you may not need to use a TVS at all. If the total charge delivered by a surge, isn't enough to push the filter cap over the limit, then who cares?
This is the basic protection that most SMPS have: they don't use MOVs, and have a relatively large (a few hundred uF at 400V) capacitor across the line, which is capable of absorbing the surge current. Surge protectors can be designed this way, as well.
So, by all means, please put a fuse in the thing -- whether it's got a protection device or not! Beyond that, don't worry. It'll probably last ten years as it is, or you can put an MOV on there to have it last five years instead (an ordinary MOV is more likely to fail than the transformer), or a stupid huge MOV (or array of TVSs -- $$$) to have it last some decades.
Tim