Elliptical orbit for Sputniks was chosen because it was easier to achieve, i.e a single burn was reqiured instead of utilising the need for the second burn for the orbit circularization.
Note (as also mentioned in the other answer) that the "second stage" of R7 rocket was ignited together with the four boosters at liftof, and also Sputnik-1 was the third ever successful launch of R7 so perhaps at the time they just didn't want to mess up with the need to allow for second stage reigniting in orbit. The rocket's primary role was ICBM, after all.
I couldn't find sources that explain why the apogee was so high, but it was definitely intended and calculated pre-flight.
I could only assume that being at so early stages of R7 development, they just squeezed the maximum out of the rocket.
In fact, specifically for Sputnik-1 the R7 mass was reduced by 7 tons:
Translated from Russian:
Compared to the standard R7 rockets, the mass of М1-PS [the rocket serial No.] was greatly reduced: massive warhead was replaced by the satellite transition part, the radio control system equipment and one of the telemetry systems were removed, the engine shutdown automation was simplified.
Mikhail Tikhonravov worked with Sergei Korolev to solve the problems of rocket design for space exploration.
The reason for elliptical orbit of the first Sputnik is described in his memorandum "On the artificial Earth satellite" (1954) (in Russian).
Translation from Russian:
The simplest automatic satellite can be considered as the first stage in the creation of more advanced and complex satellites.
The simplest satellite can move in elliptical orbit, which is easier to achieve than the circular, whilst circular orbit would have been most suitable for a satellite station [meaning more sophisticated spacecraft, probably even habitable]. It can be shown that to achieve circular orbits, it is advisable to divide the 'active section' of the flight into two further parts; the most economical in terms of energy costs is the following path. The 'active section' is chosen so that the velocity vector of the "product R" [codename for the R7 rocket] relative to the center of the Earth at the end of the first part of the 'active section' is perpendicular to the radius of the Earth. The magnitude of the speed after the end of the engine burn should ensure the satellite moves along an ellipse with apogee equal to the height of a circular orbit. The perigee of this ellipse will coincide with the point at which the engine burn finishes. At the apogee of this ellipse, additional [after]burn is performed, which would result in the satellite entering a circular orbit or into an orbit close to circular. If, for the simplest satellite, we do not perform the [after]burn at the apogee of the ellipse, (where the need to perform such a burn would have required to: a) accurately determine the apogee point; and b) orient the satellite [meaning to arrange for provision of ability to control the satellite attitude] correctly at this point), then we obtain motion along elliptical orbit that [as described above] would be transitional for a satellite intended for a circular orbit.
For 3000 kg satellite the following elliptical orbit parameters were calculated:
Perigee 170km, apogee 1100km, estimated number of orbits: 300.
In 1957, the originally planned heavy satellite (with scientific package) was running way behind the schedule and as USSR was fearing that USA were going to launch artificial satellite first, decision was made to launch the "Simplest Satellite", which Sputnik 1 was.
For this smaller satellite, the estimated planned orbit was 223 by 1,450 km, but R7 rocket underperformed during the launch and this resulted in Sputnik-1 apogee approximately 500 kilometres lower than intended.
The reasons for elliptic orbit (with high apogee) of Sputnik-2 and Sputnik-3 were presumably the same.
Orbit trajectory calculations for the first Sputniks were performed by Georgi Grechko.