It's a Cellar -- Not a Basement

This is a picture of an old-style cellar door, often referred to as a bulk-head.   In earlier days, the Dayton House almost certanly had a trap-door like this.  Eventually it was covered by what is now the side porch and the access is covered with a trap-door that is not unlike the one shown above, except that it is flush to the floor and covered with linoleum.  Old exterior basement doors are/were susceptible to rotting and rusting, and many of the old wood doors that still remained exposed to the elements end up ultimately being replaced by steel doors.   Keeping the doors in good condition is a crucial part of protecting a cellar from moisture, cold air and debris.   Luckily, the doors in the Dayton House are protected by a porch.

Modern steel doors look more like this:

Here’s an example of a bulkhead on a home near Delaware Park (66 Agassiz Circle, near the entrance to Medaille).  I picked this one as an example because it’s attached to a brick house and it is likely a configuration that existed on the Dayton House at some point.

Aside from the style, the type of foundation stone (cut and structure) along with the raised elevation marks this as home built much later than the Dayton House.

The trap door on the Dayton House is a very rudimentary form of access to a very rudimentary cellar.  The below-grade area of the house is not finished and never could be.  Aside from the fact that the foundation is a stone water table which is designed to attract moisture from the ground, finishing the basement and improving the access would make no sense.  Modern/current building code requires that furnished basements have two points of egress, which would mean either serious excavation, or a loss of living area to provide access directly through another point in the house.

In short, there is no reason to consider the type of entrance to the cellar as a problem.  The style and configuration is about the best that can be done for the style of cellar under the front portion of the house.  The below grade area of the home is the ideal place to locate the boilers and hot water tank and perhaps a stash of fine wine.  But other than that, its access is best left as is.