Arguing that attorneys at the nation’s top law firms need higher salaries may be a tough sell. But at a time when many big firms are operating more like corporations, the question is whether compensation for their chiefs should become more corporatelike as well.

As law firms have spread their reach across the globe to meet clients’ needs, the role of law firm chief executives has become increasingly critical and burdensome. Far-flung offices in Asia, Europe and on both U.S. coasts require firm leaders to spend much of their time living out of suitcases, wooing clients and creating cohesiveness among firm branches.