Moreover, the actual quantifiable impact (taking emotion out of the equation), is negligible compared to so many other issues, like the state of the NHS, or police funding or changes in legislation for health and safety - as just a few examples.
But we don't receive information without emotion. We receive information from the news media. And the news media is driven primarily by ratings, which are impacted by emotion.
The common and everyday are not news. If a person walks too close to a dog and is bit, that's not news. That's just the dog behaving as a dog does. If a human being bites a dog, that is news. That doesn't happen every day. Now, in aggregate, the danger from dogs biting people is greater than the danger from people who bite dogs (who may also bite people). But who can argue with locking up the one lunatic who goes around biting dogs and people?
Terrorism also involves a rare event: violence directed for political reasons rather than personal. It's true that the danger from mundane crime is greater than that of terrorism. But there aren't so many obvious fixes for mundane crime. There are obvious solutions to terrorism that comes almost entirely from a single group of people, primarily first and second generation immigrants. And since the media makes sure that we know of each terrorist incident, we spend more time thinking about it.
In the last week, the United Kingdom experienced one terrorist incident, killing five people (including the terrorist). The UK experienced 573 homicides total in 2015, more than one a day. So chances are that in the same week, at least seven people were murdered more conventionally. If we went back to the last terrorist incident before this, that number would likely become more lopsided and there'd be more murders than injuries due to terrorism.
In 2013, 1713 people died in car accidents. That's three times as many people as died from murders of all types in 2015. But again, accidents have many causes which are hard to address.
Terrorism may not be getting worse, but it could. There have been several terrorist incidents that were worse than the most recent one in the UK. For example, thousands died in the US on 9/11. That single event killed more people in one day than die in the UK from murders and car accidents combined for a year. Should we wait until after that happens (again)? Or proactively avoid it?
For instance, if I were to propose a tax increase for everyone of some small amount, with the aim of increasing NHS funding - how popular would that be? Now, if I were to propose barring all immigration from certain countries with the aim of reducing these rare terrorist incidents, how popular would that be?
But your small tax increase is a cost. What is the equivalent cost of barring immigration from certain countries? Many feel that immigration already costs:
Vetting immigrants requires time. Some number of government employees do nothing but vet immigrants from the relevant countries. In a ban, you can either move those people over to cover other immigrants, or you can lay them off and use the funds to increase NHS funding.
Immigrants will use some level of government benefits. Will the increased taxes they pay entirely offset this? Statistically yes.
But should we give all the increased taxes to the immigrant? Or is the immigrant displacing someone else from receiving the same job? And that hits at least twice. Once because it reduces the benefits of immigration (more taxes). And a second time because it harms the person who would otherwise have gotten that job. Perhaps a third time because wages for other people are lowered, although that gets dicey--the industry has to be rather immigrant specific.
It is clear that a broad-based tax to increase National Health Service (NHS) funding will involve paying a tax. That cost is clear. It is less clear that modest increases in NHS funding will save lives. It may be true, but it also may not. It's very difficult to measure, as what is needed is a way to study what happens with a little extra funding versus without it. And people tend not to like real experiments, e.g only giving half of people extra care.
For example, a quick search finds thousands dying of kidney problems. The recommended solution is for nurses to provide more water to patients. How much would that cost? The water cost is trivial. The really expensive part is having the nurses serve it. But nurses already visit patients. How much extra time would it take to give them water? That article has no idea.
Note how the article engages in the same kind of emotion tugging in favor of its policy as immigration opponents use in favor of theirs. 40,000 deaths! That's a big number. Mostly caused by side effects of surgery is almost hidden in the article. Can be caused by dehydration. Nurses should give patients more water! But they don't say how many deaths are caused by dehydration versus how many are caused by side effects of surgery. The implication of the headline is that all 40,000 deaths are caused by dehydration.
The real question is how much will additional funding to NHS reduce deaths? If the newly hired nurses still don't push water on their patients, it might not reduce deaths at all. If the current nurses start pushing water on their patients, we might not need the additional nurses (note that this problem involves someone getting sick at the hospital and requiring a longer hospital stay and expensive treatment; fix the problem and you free up funding to address other problems).
Policy is hard. It requires a real attention to detail. Politics is easy. It can operate through tugging emotions. After all, once you win, you can always figure out the policy, right?
If you want people to pay more attention to facts and less to rare events, then you need to start a news organization that is fact-based and gets people to watch it. Simple to say; hard to do.