The simplest way to improve the H-1B system is to abolish it.
The better but slightly less simple way is to abolish it (and a bunch of other employment-related visa categories), but also allow individuals who aren’t personally barred from entry because of past misconduct, etc., but who are not eligible (or wish to bypass wait times) for admission under other existing visa categories to pay an fee (which others, including employers, can subsidize if they wish, but gain no special power over future status by so doing) for a limited term, renewable employment-eligible status that becomes eligible to transition to permanent residency automatically after a set time in status. (This also fixes a number of other problems in the immigration system beyond the H-1B.)
The better but slightly less simple way is to abolish it (and a bunch of other employment-related visa categories), but also allow individuals who aren’t personally barred from entry because of past misconduct, etc., but who are not eligible (or wish to bypass wait times) for admission under other existing visa categories to pay an fee (which others, including employers, can subsidize if they wish, but gain no special power over future status by so doing) for a limited term, renewable employment-eligible status that becomes eligible to transition to permanent residency automatically after a set time in status. (This also fixes a number of other problems in the immigration system beyond the H-1B.)