How Proof-of-Work Challenges Change the Economics
Computational challenges take a different approach from behavioural verification. Rather than trying to determine what a client is, they make requesting the resource cost something, and let the cost do the filtering.
The client is asked to spend computation
The server issues a problem that has no shortcut and must be solved by trying candidate answers, while verifying a submitted answer takes almost no work at all.
Searching for an input whose hash meets a stated condition is the usual construction, because the search cost is tunable by adjusting the condition and verification is a single hash computation.
The client solves it in the background and submits the answer with its request. Nothing is asked of the user and, when the difficulty is set appropriately, nothing is noticed by them either.
Cost scales with volume rather than with sophistication
A single visitor pays the cost once and it is negligible. An operation making requests at scale pays it on every request, and the total becomes a real infrastructure expense.
This is the property that distinguishes the approach. It does not care whether the client is a real browser, and it cannot be bypassed by presenting more convincing signals.
Against low-volume, high-value abuse it does almost nothing, since an operation making a handful of requests absorbs the cost easily. It is a volume control, not an identity check.
Difficulty has to be tuned against the weakest client
The same problem takes far longer on an old phone than on a current desktop, and the ratio between them is large enough to matter.
Setting difficulty so that automation is meaningfully burdened can mean a several-second wait on the slowest devices, which falls hardest on users with the least capable hardware.
Adaptive difficulty based on the current risk score is the usual compromise, so only suspicious traffic pays a significant cost while ordinary visitors pay a token amount.
Attackers have better hardware than users do
The awkward fact is that a determined operation can run on hardware far faster than a typical visitor's, so the cost ratio can run the wrong way.
Memory-hard constructions reduce this by making the problem depend on memory bandwidth rather than raw computation, which narrows the advantage specialised hardware provides.
Even so, the mechanism works best combined with rate limiting and scoring rather than alone, since its guarantee is about cost per request rather than about who is making them.
Battery and energy cost are real objections
Computation on a phone consumes battery, and a site that imposes it on every visitor is spending its users' energy to protect itself.
This is why difficulty is usually kept near-invisible for traffic that looks ordinary, and why the technique is more commonly used to gate expensive endpoints than to gate access to a site as a whole.