The Doctor is a holographic program and runs off the computers processing power. Why then would he need time to make decisions and do research at the same pace as a person?
His brain should run faster than anything we would see as possible, and he is an Emergency Medical Hologram, so he needs to make decisions as quickly as possible for the emergencies he's programmed for.
So why would he be programmed with mere human response times?
As mentioned in the question, the Doctor is an Emergency Medical Hologram:
The Emergency Medical Holographic program (EMH) was a sophisticated hologram developed in the early 2370s by Starfleet and used on most Federation starships in the late 24th century. It was designed to provide short-term advanced assistance during emergencies in sickbay to the extent of literally replacing a starship's medical officer.
He's meant for situations like in the first episode, and we see him staying calm, reacting about as fast as can be expected1, and knowing what to do for each injury.
1 His physical reactions have to be kept in the realm of believability for humans, since he would be expected to work alongside them in such situations. If he, say, walked/ran at twice the speed humans were capable of, he'd be getting in the way of normal humans that can't move that fast - he looks human, and in emergencies there's no room for uncertainty.
Here's a bit on what's been programmed into the EMH:
The EMH Mark I was first activated in 2371, and was programmed with 5 million possible treatments from the collective information of 2000 medical references and the experience of 47 individual medical officers. The EMH was also supplemented with contingency programs and adaptive programs to learn while serving as a supplement of a normal medical staff in cases of emergency.
...
Dr. Zimmerman, proud at his achievement, decided to program the EMH with both his physical and psychological likeness. The resulting hologram was arrogant and irritable, and as a result was poorly received by many Starfleet doctors.
On the "mental" front, his base programming is around applying and adapting what's already been programmed into him. Researching entirely new solutions to unexpected problems isn't something the EMH was supposed to ever be doing, that was the job of the ship's doctor. (And Zimmerman's own personality may have been unintentionally inhibiting him...)
The Doctor only started learning how to expand his programming at Kes's urging and Janeway's insistence that he acts as the primary doctor. Given that it's gone wrong at least once before, most likely he's just been given inefficient algorithms due to B'Elanna's inexperience in that particular type of research. (She's an engineer, not a doctor, after all..)
And as a final tidbit, computers in general are just bad at certain classes of problems. The complexity of something as simple sounding as the traveling salesman problem is unexpected to people unfamiliar with it. So something like open-ended research that requires waiting for physical responses when testing, means he has to exhaust as many possibilities as he can before choosing the solution he thinks is best before he tries it on a patient. I would guess that, most likely, the Doctor is thinking of and discarding an enormous number of possibilities before he comes up with a useable idea. This would mean it only looks like he's operating at human speed.
P ≠ NP... ;)
Researching doesn't just mean looking stuff up. Imagine you needed to know how much sugar can dissolve in a certain volume of water, and how that varies with temperature. You can just look that up, there are tables for it. But if instead of sugar it's some alien fungus you've just found on a planet, you have to actually run experiments, grinding it up and stirring it into the water and so on. You may have to create cell cultures and let them grow. That stuff takes physical time no matter how smart you are.
For the most part, the Doctor has access to the same modes of research as any other crewman - the only part he is able to shortcut is the actual reading and interface.
The thing is, most of the research is done via computer search, and the rest by practical experimentation.
Computer research is computer research - sure, he's faster with the interface - but that's not a substitute for the time taken for an individual officer's routine priority on the central processing cluster - which we see in every Trek series is fast, but often not fast enough. And we see that the EMH does computer research slightly faster than his biological assistants do - less creatively, but slightly faster. In other words, interface time issues.
As for practical experimentation... the limit on speed for that is whatever process you're investigating. If a bacterium, you have to culture and cultivate it... and that only happens at its speed, not yours. If regenerating burns, you can't test faster than the thing works. If observing the effect of a particular chemical on bone density, you can't progress any faster than the bone growth rates.
And most of the EMH's experiments combine both. In one mode, he's just another high priority officer - and not even that until later on - and the other, he's not the speed-limiting factor.
His matrix though advanced is like any other computer program and hardware, there's a limit to what it can process, and how much it can store. In 'the swarm' the doctor exceeds his memory capacity causing a cascading failure. One of the options for repairing him is a memory upgrade.
The doctor is effectively a huge interface for the special EMH medical database (a combination of medical publications and the personal experiences of 47 physicians). It is stored in the holographic memory system which he has direct and instant access to.
Anything else not stored in the holosystem, would be in the general ship's database, which would have to be accessed and researched indirectly, a process that would take time.
Though holograms appear to be very advanced, they are extremely limited. The individual matrix can only store a small amount of information, with the rest being stored in the main holosystem memory or main computer system memory. In 'message in a bottle' transferring the medical library to a hologram caused it to overload and fail.
Though the doctor is much more advanced, he is ultimately limited by the sickbay hardware and his own matrix.
