One possible factor was that styling director Ray Dietrich was eased out of his job in 1940 following the death of Walter P. Chrysler. He was replaced by Bob Cadwallader, more an administrator than a stylist. Cadwallader's influence became strongly manifested in those 1942 grille designs. However, both men were subservient to Chrysler's engineering leaders, unlike, say, Harley Earl's dominant position at General Motors. So assigning credit or blame regarding Chrysler styling in those days is more difficult than at, say, GM or Ford.
Another factor regarding those 1942 grilles is that the basic car body design appeared for the 1940 model year. By 1942, it was time for a stronger facelift. Yet another consideration is grille design fashions. The late 1930s and early 1940s saw American grille orientation moving from vertical to horizontal for most car brands. As shown below, Chrysler followed that trend to the point where especially DeSoto and Chrysler grilles were even more horizontal than the norm for those days.
Post- World War 2 Chrysler brands were given redesigned grilles. Those designs remained essentially untouched through the early part of the 1949 model year, thanks to the postwar seller's market for automobiles.
1940 Plymouth DeLuxe 4-door sedan - car-for-sale photo
A simple design featuring horizontal chrome strips punctuated by a vertical "prow" divider.
1941 Plymouth Special DeLuxe Coupe - BaT Auctions photo
The 1941 facelift featured curved framing.
1942 Plymouth Special DeLuxe Coupe - car-for-sale photo
Considerable front-end reshaping for '42 including moving the headlights slightly inbound. Stronger grille bars extending over a wider area while upper framing covers part of the previous prow.
1940 Dodge 4-door sedaan - car-for-sale photo
Curved framing for thin bars overlapping the prow area. There's a mid-level band of painted sheetmetal.
1941 Dodge Custom 4-door sedan - Mecum Auctions photo
The prow returns while the framing assumes a different shape. Clearly more horizontal than the centralized '40 design.
1942 Dodge Custom Convertible - Mecum
Headlights move towards the center while the grille becomes bolder, more geometrically framed. Thin vertical bars are set behind the horizontal bar creating a subtle "egg crate" effect. Bars flow over the prow.
1940 DeSoto Touring Sedan car-for-sale photo
Curved framing similar in spirit to the '40 Dodge and '41 Plymouth. Extremely thin horizontal bars. The grille encroaches on the prow, but not quite -- there being a bold, vertical, chromed separator bar.
1941 DeSoto - Auctions America photo
New front fenders. Grille bars much wider and now vertical (a DeSoto recognition feature that continued through the 1955 model year).
1942 DeSoto DeLuxe 4-door sedan - car-for-sale photo
The Famous 1942 DeSoto front end. Headlights towards the middle, but covered by doors. Bold, vertical grille bars topped by a horizontal framing strip that extends across the length of the front fenders. There's a prow, but it's almost completely obscured.
1940 Chrysler Windsor Convertible VanDerBrink Auctions photo
Somewhat similar to the '40 Plymouth except that the bars flow over the prow.
1941 Chrysler Windsor Highlander Convertible - BaT Auctions
Fewer, thicker bars that extend a short way beyond the sides of the radiator opening. The prow is now emphasized by a vertical chromed bar.
1942 Chrysler Windsor Coupe - car-for-sale photo
Another famous grille design. Again, headlights more centered, the prow de-emphasized. Here the grille bars wrap all the way around the fender to the wheel opening while the upper frame continues the length of the fender.