In the US 30 year fixed rate mortgages are common (standard?). Rates have also bumped around record low territory for years.
I know people who refied into 15 year fixed, but the rates have typically been so close I didn't see the point. Just pay more each month on your own and avoid the costs of the refi.
Rates might have little to do with whether refinancing from 30-year to 15-year makes sense. The most important factor is how long you plan on living in the house compared to the difference in interest paid between the two amortization schedules during that time. The longer you stay in the house, the larger the difference to where paying refinancing fees is virtually free.
On the typical fixed rate loan, amortization schedules are a function of rate, time, and payment. If someone wants to accelerate the schedule, they just need to pay more principal each month.
So, if someone already has a 30 year and the 15 year rate isn't much different, refing into a 15 isn't necessary. Just start paying monthly like a 15 and it will get close enough.
Also, if I already had a high rate loan and was refing where the 15/30 rates are very close, I would go 30. That way I can pay it like a 15, but have the flexibility to pay less if, for example, I lost my job.
Finally, this is why it's common to make 1 extra payment each year as it will shave ~4 years off the end of the loan.