It's an amenity Amtrak offers to compete against other transportation providers. Most bus carriers on the NEC offer free wi-fi, so offering free wi-fi is a way for them to not lose as many of those customers. Frankly, if Amtrak didn't offer free wi-fi I would expect to see a fair amount of defections to bus services, as it would become a "wifi vs. speed" question between the bus carriers and Amtrak. Right now it's a "pay a bit more to get there faster and more comfortably" question...Amtrak shouldn't try and give people a reason (other than price) to choose the bus companies on the NEC.
Also, how much money would there be to be made on offering wi-fi? Most people who need connectivity have a cellular hotspot already, and since Amtrak travels on the ground cellular connection would be available for most of the trip (at least as far as I'm aware.) Thus, Amtrak would need to offer either a better product than LTE (which would be difficult on any sort of shared connection) or price it cheaper than LTE. Current overage costs on many plans are about $10-$15/GB, so unless someone is really pushing the connection I don't see more than a gigabyte being used on most NEC journeys. Thus, whoever would provide it would have to price it at or below that in order for people to defect from their LTE connection to AmtrakConnect. I don't see there being much profit margin there; I highly doubt there'd be enough for a private investor to want to take on the risk of wiring all trains for wi-fi and putting their own backhaul in (which is not cheap.)
Also, satellite broadband would be a terrible idea for the NEC. Bandwidth is extremely constrained, the cost of bandwidth is similar, and it has much higher latency (so everything feels slower.) Satellite internet would also require a constant re-tuning of the dish, which probably wouldn't be difficult but may cause some intermittent dropping moving from satellite to satellite. Cellular is a much better option, and if they could create their own network along the NEC the network would be orders of magnitude better than any current satellite connection.