You have correctly surmised that politics played a part in Eisenhower opting to go for the broad front, but a much larger part was played by logistics. Simply put the Allies outpaced their own logistics, and all operations that could've alleviated the situation in 1944 failed.

By late summer of 1944 the Allies had advanced through France and to the German border with magnificent speed, driving the Germans in front of them all the way from Normandy. When the British 11th Armoured Division captured Antwerp on the 4th of September it had advanced almost 350 miles in just six days.

However this rapid advance came with its own problems for the allied armies were still mainly supplied through the port of Cherbourg all the way on the tip of the Cotentin Peninsula. The Overlord plan had called for the capture of the port cities of St Nazaire, Lorient, and most importantly, Brest to help supply the advance of troops, but with the sweeping advance of Operation Cobra and the breakout out of Normandy, the important ports in Brittany and the Western coast of France had still not been captured. In fact, Brest would not be captured until the 19th of September, after costly urban combat that in the end proved somewhat useless as the Germans had successfully destroyed the all-important port facilities during the protracted fighting. With this in mind the ports of Lorient and St.Nazaire were simply put under siege and wouldn't surrender until the spring of 1945.

To alleviate this supply problem, and the long, long route that "the Red Ball Express", had to take from Cherbourg, the capture of Antwerp became critical, which, as I said previously, was done on the 4th of September. Fortune seemed to be with the allies, as the city was captured with the port facilities intact, which should've helped with the supply problems. However, the shipping lanes to Antwerp were guarded by the Scheldt estuary, an area of marshland, islands and other unfortunate things. To make Antwerp available for supply and shipping this area would have to be cleared, and the Germans were dug in tight. The Canadians would have to clear the area by amphibious assaults over rivers and flooded fields, as the Germans had destroyed the dams and dikes in the areas. In addition to this, the British didn't initially seem too bothered by the area and thus failed to concentrate forces for the operation immediately after capturing Antwerp, giving the Germans more time to prepare their defences. In the end, Antwerp wouldn't be safe for allied shipping before mid-October.

Thus all the way until the late autumn/early winter of 1944 all allied supplies on the Western Front had to be shipped to the, relatively small, port of Cherbourg and then transported 400 miles to the frontlines in trucks.

This meant that even if Eisenhower wanted to concentrate his forces on an offensive somewhere, it would mean that all other areas of the front would have to simply stop for the time being. This in turn led to problems of politics between the different characters in Allied High Command, and the Anglo-American tensions didn't help too much either.

Of course, it didn't help that the one time Eisenhower gave in to his generals demands for a a schwerpunk, as you put it, the operation failed miserably. Even if Market Garden didn't prolong the war (in my opinion, it simply failed to shorten it), it proved to Eisenhower and SHAEF that it was better to take things slowly and wait for the supply problems to be sorted, than risk men and materiel in potentially unsuccessful offensive pushes. Afterall, every single Lee-Enfield, Garand, Sherman, and halftrack lost in such operations would also have to be replaced via the strained supply lines.

Meanwhile the Germans, quite like you, were rather perplexed by the Allied refusal to make a concentrated push and welcomed this with relief, as it gave them time to reorganize their forces. This in turn would later let them launch their last great offensive of the war in the Ardennes in December.

Sources:

Roland G. Ruppenthal, Logistics and the Broad-Front Strategy

Antony Beevor: "The Second World War", "D-Day", "Arnhem", and "Ardennes", simply because they were literally within reach.

Edit: Had to fix some Reddit-bugs that mangled my answer.

u/AnarchoPlatypi has this mostly covered, but I wanted to add that it is an oversimplification to claim Eisenhower favored a 'Broad Front' Strategy while Mongomery favored a spearhead thrust. That view is probably based more on the actual result than Eisenhower's plan.

Eisenhower was presented with three plans (ignoring the overly pessimistic plan from SHAEF G4) after the combat around Falaise. The first plan from the SHAEF planning staff most closely resembled a broad front advance as they wanted to keep the pressure on the Germans and not give them time to regroup. More specifically it was a double pincer with Montgomery's 21st Army Group following the Rouen-Amiens-Brussels-Dusseldorf axis, and Bradley's 12 US Army Group advancing via Metz and the Sarre towards Cologne. The problem with this plan was it completely ignored logistical constraints.

Montgomery's plan was a massive 40 division push along the channel coast. It had the advantage of a concentrated push, would clear the V1 and V2 rocket sites, and potentially have the allies across the Rhine and taking the Ruhr. The big downside in Eisenhower's view was that it would leave a 450km long right flank that stretched from Reims to well past Cologne. The plan was that the US 3rd Army would need to redeploy to cover this flank although it meant traveling farther than if they just advanced forward and shortened the flank. The other downside was that it was too focused on crossing the Rhine and not focused enough on opening the ports at Calais and Antwerp.

Patton's plan was to send four Corps east towards the Rhine, Karlsruhe, Mannheim and Weisbaden.

The plan that Eisenhower decided upon was indeed a compromise plan that looked much more like Montgomery's plan than any of the others. The advance along the Channel Coast made the most sense, but more resources needed to be diverted towards opening the Channel Ports, and a limited advance by Bradley to head towards Metz and Nancy. Montgomery instead of crossing the Rhine would advance to the Rhine between Arnhem and Cologne.

By September 11th the reality looked much more like a broad front as Bradley had advanced past his objective to Metz and Nancy while Montgomery was short of the Rhine on a line leading east of Antwerp. Supply was the biggest issue in the advance, but the allocation of supply and transport was based on the original plan, how many divisions were involved and how far they were expected to advance, so the lion's share of supply was being sent to Monty.

Patton was largely responsible for the speedy US advance. He was ahead of his time for the US Army in pushing much of the supply responsibilities from the Army HQ down and assigning supply trucks to the division level. As one Red Ball Express driver said, when Patton jumped on the back of a truck and began unloading supplies no soldier stood around. That doesn't mean Patton didn't have supply issues as they also suffered from the inability of ComZ and ADSEC to move supplies from the ports and beaches. The 3rd Army was always fastest in advance, but they were also constantly out of supply.

As previously mentioned, the failure to open the port at Antwerp and the Scheldt estuary was the bigger problem. The failure to seal off the Scheldt also meant that 80,000 German troops managed to cross from the south bank to the north and further strengthen the defenses there. At the Oct 5th Combined Chiefs of Staff meeting, ADM Sir Bertram Home Ramsay was furious with Monty for the failure to open Antwerp and the Scheldt. Field Marshal Alan Francis Brooke also saw this as a failure on Monty's part, although Eisenhower took responsibility for the failure at the meeting as he had approved Market Garden prior to fully opening the port at Antwerp.

Sources:

Aubin, Nicolas Liberty Roads - Red Ball Express

Danchev, A & Todman D. (Ed.) War Diaries 1939-1945, Field Marshal Lord Alanbrooke