I usually shoot portraits hand held...
In the studio, it is absolutely no problem because the electronic flash freezes all camera shake and subject movement.
Outdoors, I have no problems with holding the camera steady and usually for portraits, the subject isn't moving at all.
Now for your question as to the height of a tripod.
I use two tripods because I just haven't found one that will fulfill all of my needs.
The Giottos MT-8180 is a tall and sturdy tripod that easily expands up to a height I can easily use (I am 6'1" tall) and this tripod is extremely sturdy allowing me to use a Manfrotto 393 gimbal mount with a 400mm f/5.6L lens with ease. The rig could support a heavier package if I ever decide to get a heavier lens/camera combination. The MT-8180 also articulates fully allowing me to place my camera just about anywhere for macro or close-up photography. When I am shooting in this mode, I use the Giottos MH-1300 head with the MH-657 Arca Compatible QR.
The Giottos is an extremely solid tripod. I recently used it in what felt like gale force winds at Bryce Canyon, Utah. It had no problems supporting my camera/lens. However, although the MT-8180 is carbon fiber, it is too heavy for me to carry everywhere - especially when boonie-tromping.
I use a modified SLIK Pro 330DX tripod for boonie tromping. I replaced the long center column with an optional shorter column (present black colored 330DX tripods are equipped with two piece center columns so you can have a choice of using in in a standard or shorter mode). With the shorter column installed, the legset weighs exactly 2-pounds without a head.
I switched from the standard SLIK pan-tilt head to an 11-ounce Adorama Flashpoint Magnesium Arca Compatible Ball Head. This little head is fully capable of supporting a 40D and 70-200mm f/4L IS lens which is the heaviest package I ask it to support. The legset is also capable to supporting that package.
Sure, it is shorter than I would really like (49" with head and without center column extended). But, I have no problems either stooping a little (the height of the camera adds a few inches to the level of the viewfinder) or I will use my right angle finder. Since I am an old twin-lens-reflex user, I am very comfortable with looking down to compose my shots.
I would NOT choose this tripod as my only one. Being short, it is difficult to follow moving subjects and the tripod doesn't allow much flexibility in camera placement. However, for my uses it is great. The Arca Compatible ball head allows me to use a RRS L-bracket which mounts a non-tripod ring equipped camera/lens more securely. This is especially true in the portrait position where the L-bracket keeps the camera right over the apex of the tripod, not cantilevered over to the side.
The tripod/head combination weighs only 2 pounds 11 ounces so I can take it anywhere and everywhere with ease. I have been using a tripod much more often since I developed this little jewel.
The tripod as I use it cost about $125 which at one time I would have considered very expensive but, is a reasonable cost for a tripod now. Other tripod/head combinations this light and this sturdy cost several times that amount.