Since it was already a tollway that was built and operated by the state, IL was able to get away with making it I-355. On the other hand, the reason the Pocahontas Parkway is VA 895 and not I-895 is because it used federal funding.
AIUI, the no-tolls policy does not apply to mileage (including mileage that was otherwise eligible for Interstate construction funds as part of the original 41,000-mile system) for which no federal funding has been used. Examples include I-335 in Kansas (not part of original system, construction originally paid for by tolls, designated 30 years in retrospect in order to take advantage of the Reagan-era NMSL increase to 65 MPH for Interstates), I-95 between Baltimore and the Delaware state line (could have been built with Interstate construction funds, but opened as tolled I-95), entire length of the Pennsylvania Turnpike (paid for by tolls), and so on.
Virginia SR 895 had no federal funds used in its construction, so what prevents its being designated as an Interstate is several million dollars of federal funds that were disbursed for design (including compilation of environmental documentation) decades before it opened. In principle eligibility for an Interstate designation could be restored by repaying these federal funds, but nobody seems to have a few spare million in loose change lying around.