Is it necessary to have a neurologist?

My FIL had dementia. We never saw a neurologist. His primary care doc saw him and we did just fine. He was 89 when his symptoms presented themselves and was way beyond any of the medications that some neurologist prescribe to slow the progression (in some people). He just wasn't a candidate and the meds had worse side effects that all of us were willing to deal with.
A neuro might be able to give you a better idea of "what's next", but probably won't be the main doctor you go to for troubles. All that said, you certainly don't want to cut ties with the neuro, simply because he/she isn't your daily doctor for advice.

I agree with Ceecee65 in not cutting ties, but I have different take on the need for a neurologist. MCI is not dementia but can be a precursor to it. The difference will be when your husband has difficulty with activities of daily living; eating, dressing, bathing, etc., which he may never have. Although a PCP can suspect dementia, he/she should refer the case to a neurologist. PCPs are not specialists in neurological diseases and typically will label dementia type symptoms as AD when they may not be. With your husbands vascular issues, I would have vascular dementia on your radar. Your PCP can order an MRI or CAT scan and bloodwork to eliminate any treatable conditions.

A one time visit to a neuropsychologist would give you a more definitive idea of what you're dealing with. I always like to visit a specialist when the issue is outside the realm of a family doctor.

My mom was under the care of a neurologist because of numerous TIAs. Neither he nor her previous neurologist or our family doctor ever mentioned that vascular issues can lead to vascular dementia or explained the significance of her MRI (which the family doc said "lit up like a Christmas tree"), I had to find out about that by searching the internet trying to figure out what was happening to her. So my take is that while neurologists may be helpful, it's only if they specialize in dementias, and then only if you find the right fit.