Icelandair doesn't charge to reserve a seat.
OK, I guess I remembered wrong, Icelandair offers "economy light" with a charge for bags but not seats.
http://time.com/money/4970571/airline-fees-icelandair-europe-checked-bag/
And the website:
Economy Light
Included
Carry on up to 10kgSeat reservationIn-flight entertainmentSoft drinksEarn points
But it is easy to figure out that if you want to check a bag, it's cheaper to "buy up" to standard economy then pick "economy light" and pay for the bag later.
As to Delta, here's what comes up for London "Basic Economy" where a seat cannot be reserved in advance, even for money:
ON YOUR FLIGHT TO LONDON-HEATHROW, UNITED KINGDOM
A Better Value Fare In Basic Economy
Enjoy the benefits of a Main Cabin experience at a value fare. Though some restrictions apply to your fare, you will still enjoy our award winning services in-flight, including available Wi-Fi and complimentary Delta Studio® streaming on your device or seatback screen. You also enjoy your choice of refreshments, including complimentary snacks, juices, Starbucks® coffee and Coca-Cola® products on flights over 250 miles.
FROM
$895 .91
Round Trip Per Passenger
Restrictions Apply
First checked bag is not free
Seat assigned at gate or after check-in
Seat assignment may not be together with traveling companions
Not eligible for refunds