A night crossing would have been an utter disaster for the Germans in 1940. They'd have scattered their shipping and troops all over the place and a coordinated landings would have been nearly impossible. The Allies only managed to pull off a night crossing in June 1944 due to intense preparation, the use of carefully-placed beacons from the COPP, and much more. And even then, the Normandy landings were executed during daytime. And despite all that, an entire infantry division(+) ended up landing at the wrong beach.

As for why the Luftwaffe didn't just do a "maximum effort" sortie on invasion day ... The Luftwaffe did launch major attacks on several occasions. "Eagle Day" on August 13th, 1940 is one of the more notable examples, with nearly 1,500 sorties launched. What happened? The RAF launched a major response of its own and shot down nearly 50 German aircraft.

Trying to launch a major air offensive on invasion day would just have lead to an aggressive response by RAF fighters. And even though the RAF was outnumbered, British fighters flying from England could sortie, land, and sortie again multiple times in one day, while the Germans flying Cross-Channel could realistically only do one mission per day.

Having more planes therefore didn't necessarily guarantee the Germans overwhelming air superiority. Sure, they might have more planes, but the RAF had the Chain Home radar network for early warning, a greater ability to fly multiple sorties in a day, and other force multipliers that let Fighter Command punch well above its weight. Trying to beat the RAF on invasion day wasn't going to work. Plenty of RAF bombers and fighters would still be left to fight on day 2, and day 3, and so one.

If the RAF was going to be neutralized, it had to be neutralized as part of a sustained pre-invasion air campaign. And yes, the RAF did have to the neutralized. Here are a few reasons why:

1) The Royal Navy - if the Luftwaffe didn't have air supremacy, or at least air superiority, they Royal Navy would have been able to send destroyers and cruisers into the Channel to shoot up the largely-defenseless German barges and transports. The Kreigsmarine had U-Boats, some destroyers, some E-Boats, and various other coastal craft on hand. They couldn't go toe to toe with the Royal Navy, and they knew it. The Luftwaffe had demonstrated their ability to badly bloody the Royal Navy at Dunkirk in June 1940 with one hand tied behind their back, so they'd be needed to sink the British warships if they sallied. But they could only do this if they had control of the skies.

2) Airborne landings - Fallschrimjaegers would have parachuted to seize key locations in the event of an invasion. They'd already done this in the 1940 attacks on Norway, Denmark, and the Low Countries. However, they needed large numbers of slow transports and gliders to execute the attack. They'd be sitting ducks for RAF fighters.

3) Fire support - Given that the Germans didn't have much in the way of a navy, naval guns (and coastal batteries firing cross-Channel at "Hellfire Corner") couldn't much provide offshore fire support. Since it'd take time to land artillery,the Germans needed some way to support their landing troops. The obvious answer was airpower. Again, the large numbers of vulnerable bombers could only fulfill that mission if the Luftwaffe owned the skies.

4) Bomber Command and Coastal Command - In the event of invasion, RAF Bomber Command and Coastal Command would have unleashed hundreds of Blenheims, Beauforts, Ansons, Hudsons, and other light bombers on the German warships crossing the Channel. Medium bombers like the Wellington would have hammered German-held ports in Occupied France. Barges being loaded with the second and third waves would have been sunk. Supplies would have been destroyed. If hundreds of German fighters were busy protecting German bombers attacking England, then there wouldn't be enough fighters left to stop all the British bombers. Only if the Germans had control of the skies could they concentrate their efforts on destroying any concerted British bomber attack on the invasion force.