This is a fundamental feature of why free-flying occulters are considered for exoplanet searches. The closer the occulting screen is to the telescope, the more pronounced two problems become:
SOHO, of course, uses external coronagraphs for several of its camera/telescopes. However, the application is different because such solar coronagraphs occlude a large angular region of the sky due to the occulting disk's proximity to the telescope.
To search for extrasolar planets, one needs to be able to search within an arcsecond of a star effectively. An occulting screen must block nearly all of the light of the bright target (star), therefore it must be at least as large as the telescope aperture. If such an occulting screen is placed, say, 1-metre from the aperture of a space telescope, then indeed it could block the starlight.
But unfortunately, the screen placed 1-metre from the aperture also blocks out most of the light reflected from a hypothetical object under 1-arcsecond from the star. The entrance aperture for light from such a hypothetical extrasolar planet would be less than a 5-micron wide sliver along one edge of the telescope aperture. This is tantamount to a reduction in the brightness of the hypothetical extrasolar planet by over 14 astronomical magnitudes. The necessary collecting area of the telescope to gather enough light to see the exoplanet would be hundreds of times greater than anything possible today.
This aperture blockage problem is not alleviated sufficiently for 1-10 metre telescopes until the occulting screen is placed more than a hundred or so kilometres away from the telescope.
As if aperture blockage were not serious enough of a problem, control of the position of the occulting disk at small distances requires a more sophisticated and demanding approach with an occulter placed near the telescope. Even at a telescope-occulter separation of 100-metres, the occulting screen would need to maintain its position to a few microns at worst. Such fine alignment control probably requires constellation spacecraft metrology (for free-flyers) using interferometry. The external occulter approach on the other hand is low-tech, nevertheless aiming at controlled stellar occultations to optimize science quality for extrasolar planet searches. Science quality has been a persistent problem with attempts to image extrasolar planets to date.
Internal focal plane coronagraphs are another occultation approach to finding extrasolar planets, however they are replete with their own problems. Several have been flown in space, though none whose targets were stars outside the solar system has performed to specification, and no confirmed exoplanet image detections have been published from their use. Even the ACS coronagraph to be installed on HST at the next servicing mission will not likely outperform the NICMOS Camera 2 coronagraph, perhaps the most successful stellar coronagraph used to date.