I feel that welfare services aren't reaching everyone adequately.

Literal

Welfare [topic-は] sufficiently spread not-exists [manner-ように] think [concessive-んですけど].

十分に行き渡っていない means 'not adequately reaching everyone' — 行き渡る means 'to spread throughout/reach all corners.' ~ように思う means 'I feel/think that.' んですけど trails off softly, inviting response.