In the average Ashkenaz synagogue, the % of kohanim is around 1% to 3%.
In the average Syrian synagogue, the % of Kohanim is around 30% to 35%.
Since the Torah prohibits Kohanim from marrying converts [gerim],
is it wise to permit converts in a community where 30% of the men are Kohanim?
Additionally, some poskim [whose names I unfortunately cannot remember] have written that Kohanim who are Syrian and/or Sephardic have a greater [or better] mesorah of kehunah than Ashkenazic Kohanim, which makes the prohibition against Kohanim marrying converts even greater for Kohanim who are Syrian and/or Sephardic.
For example:
When a Syrian Kohen performs a Pidyon HaBen, he NEVER returns the money, because Syrian Rabbis hold that there is no doubt [safek] on the identity of their Kohanim.
Compare this to Ashkenaz Kohanim, who return the Pidyon HaBen money,
because they fear a doubt [safek] on their identity of their Kohanim.
Is it wise to permit converts in a community where 30% of men are Kohanim,
who have no safek [or less safek] on their yichus as Kohanim?
PS: Many Orthodox Rabbis in England do not accept converts, because Jews were re-admitted to England on condition that they not accept converts.