The double quotes are mainly for safety (good habit in case $h ends up containing an empty string by mistake, for example) and in theory, the && variant could create two external processes where -a would only create one. (It's theory because [ is probably handled internally in moderns shells, so there is no external process involved.)

Shell scripts are not parsed much, the syntax is more shallow than in many other scripting languages and this creates some complications, but also helps make the shell extremely versatile. The lack of standard, built-in arithmetic operators right from the start is another source of complexity in this case. POSIX attempts to fix some of the issues but historically, different shells have developed different extensions which have then created, as it were, even more different ways to skin a cat.