Small pox acts quite differently than measles, though. It’s not as contagious as measles is, it has a shorter time from exposure to symptoms and was more easily recognized as being small pox than measles is now because most doctors don’t see measles cases anymore. I think you’re right, theoretically it would be possible to eradicate measles, but functionally I have my doubts.
We, and as a Dermatologist I'm one of those counted on to recognize such, don't see much smallpox either these days. Smallpox should be easier to clinically differentiate from its remaining mimics than measles, but based on my observation of my otherwise bright, but nondermatologically trained, colleagues care before the patients eventually reach me I'm not confident it would be recognized promptly. In 30 years I've, maybe, seen one cases of measles and the lab work on that returned inconclusive. Of course I've seen zero smallpox cases personally, although I've been fortunate to discuss smallpox with someone who actually treated it in Iowa.
Measles should be harder to diagnose because it resembles severe cases of some fairly common drug reactions or non-specific 'viral' rashes. Smallpox used to be confused with chickenpox although the 'fine print' was different in their appearance. But most doctors now probably haven't seen chicken pox either (thanks to vaccines!) Of still existent rashes a fairly rare drug rash (AGEP) and the rare worst form of psoriasis come the closest to being confusable with smallpox. Most doctors won't have seen or even heard of either so will be prone to quickly passing them to their favorite experts as impressive unknowns. The cases of monkeypox, smallpox's remaining close cousin, were recognized that way. The tale of the local Dermatologist who figured out enough to contact CDC was fascinating. Whereas primary physicians might delay passing along something they thought was 'just' a drug rash or a viral rash.
For humans I'm not sure anything is more contagious than measles. However the basic strategy for fighting it is the same. First, maintain high enough vaccination levels so that any outbreaks that do occur aren't large enough to overwhelm local public health resources. Then, once an index case is recognized, aggressively contact trace them and vaccinate or isolate everyone conceivably exposed. IF your overall level of vaccination is sufficient and the outbreaks aren't too large it can be done. Do it enough, long enough and you'll eradicate it from regions and eventually the world. I was very impressed that medical superpower, Nigeria, was able to do it, when an infected, entitled, American ex-pat trying to return home with Ebola medically crashed in their lap. It's a lot harder when many, most or all are susceptible to the disease. The immunosuppressed population: infants, the elderly, those with immune systems depressed by diseases or by successful treatment thereof is growing and we want it to grow. Vaccinating them either doesn't 'take' or is very risky to try. As their numbers grow we can less afford additional, 'voluntary,' opt-outs amongst those medically qualified for vaccination. Unless those opt-outs as a group chose to entirely isolate themselves from the rest of humanity they risk spreading large outbreaks to the rest of humanity and suffering catastrophic outbreaks themselves once the isolation is broached.
Realistically, unless you're living on North Sentinel Island today, you're not sufficiently isolated from today's humanity to be safe for either side. You were drafted into this war at birth. You don't deserve any more choice than a person trying to escape jury duty because he's afraid some lunatic will blow up the court house. The only exceptions should be those determined by good science. The only acceptable objections are those intended to maintain that good science standard. Object if Obama, et al, comes out with vaccinations for 'global warming,' then isolate the lunatics!