I would guess 2-week turnaround and 100 launches per year would not have been feasible -- but with enough budget, almost anything is possible.
I see a few major problems raised by your bullet points, which are clear in hindsight but likely weren't obvious in 1969.
It will take only 4.3 hours to inspect the spacecraft engines.
The space shuttle main engines turned out to be extremely complex and sensitive machines. Rather than getting a quick inspection, they were removed, inspected in detail, and refurbished after every flight. In 1969, the most comparable engine was the J-2 used on the Saturn boosters, which yielded about 8% poorer specific impulse due to a lower chamber pressure, but produced almost the same thrust-to-weight ratio as the SSME. Unlike the SSME, the J-2 probably could have flown back-to-back missions without major service. From The Space Shuttle Decision:
The J-2 did even better [than the F-1], with a test engine running for 103 starts and 6.5 hours, without overhaul.
"We never wore out an engine of the J-2 type," recalls Rocketdyne's Paul Castenholz, who managed its development. "We could run it repeatedly; there was no erosion of the chamber, no damage to the turbine blades. If you looked at a J-2 after a hot firing, you would not see any difference from before that firing. The injectors always looked new; there was no erosion or corrosion on the injectors. We had extensive numbers of tests on individual engines," which demonstrated their reliability.
6.5 hours is about 45 STS ascents, so a reusable spacecraft using such engines would certainly have been able to fly multiple back-to-back missions without overhaul.
Thermal protection is radiative; no ablation. Parts of thermal protection system last 10 to 50 missions (depending on part location) before replacement or overhaul.
Ablative thermal protection was well-proven at this point, but was unacceptable for a reusable launcher. The choice of airframe material and thermal solution was hotly (sorry) debated for quite a while during the early development of the shuttle. The Space Shuttle Decision has a lot to say here also. I don't think there were any very good options for thermal protection here. The shuttle's silica tiles were lightweight and effective, but required a tremendous amount of maintenance between flights. Limiting such tiles to only the most critical areas and using high-temperature alloys over most of the spacecraft would have increased development and construction costs (which is why this strategy wasn't used for the shuttle) as well as weight, but reduced the per-flight cost and turnaround time. While individual tiles on the shuttle might last for 10 or more missions, each of the thousands of tiles had to be individually checked, at great cost.
100 launches per year
I don't see how this is possible in practice.
Every shuttle mission involved at least some of the crew training for literally years. (Payload specialists, who were not career astronauts, but instead attached to a specific mission to do something with a specific payload, only trained for months, but were a small minority of shuttle crew members.) With an increased launch cadence, presumably that training would be compressed. If a commander or pilot was flying more than twice a year, their training in mission-agnostic aspects would essentially be constantly up to date, but they'd still need to train up on mission-specific aspects. Space mission training is hard, stressful work, and takes a toll on astronaut families; very few astronauts have flown more than 3 or 4 missions.
If you assume that the training cycle can come down to 2 months (I can hear Organic Marble snorting from here), then 100 flights a year implies 16 concurrent training programs. That's 16 prime crews, 16 backup crews, 16 support crews, in concurrent high intensity training. You'd need to duplicate simulators, you'd need to duplicate all the facilities that support the training, and the headcount to support those facilities. Assuming 2 weeks as a typical mission duration, you'd have to be able to control at least 4 missions concurrently. (Although, at that launch cadence, you're probably flying shorter missions, especially since you'd need a much smaller and cheaper orbiter than STS.) You'd need many more astronauts, and they'd burn out in 2 years instead of 5-10 years. You're going to be hiring a lot of people, and that means they're not all going to be the best of the best. If you want to be able to deal with one launch slipping without pushing all the other ones along with it, you need still more concurrency.
STS had a 98.5% safety record -- 2 spacecraft and crews lost out of 135 flights. With this cadence you'd be lucky to only lose one a year.
Note that all the steps you can take to increase cadence -- less efficient engine, more heat sink and less tile, simplify & shorten each mission -- point towards a significantly lower total payload mass, as well as payload mass ratio, than the STS. One relatively easy and sensible step to take to try and address this, that I wish the real space shuttle program had done, would be to make two versions of the orbiter: one uncrewed to be used for pure satellite deployment work, one crewed for missions that really needed a crew. There's an interesting alternate history in that.